Whether they would describe themselves as socialist or not, I have never come across any record. However, it would not be out of place to assert that the Métis Rebellion was a mass political movement for the people's control of the land and resources against the onslaught of industrial capitalism.

To provide a little context: in the 1860s, the Northwest was the heart of a struggle between two economic orders: the old feudal system governed by the Hudson's Bay Company, and the new system of industrial capitalism governed by Ottawa. British industrialists and financiers had cemented their position in Eastern Canada, and came into conflict with the HBC as they sought to expand their sphere of influence Westward. This came to a head when the government in Ottawa extended constitutional authority to purchase Rupert's Land from the HBC in 1869 (with promises of massive payouts to the major stakeholders). Essentially, the HBC had previously had legislative authority over the area, and now they had accepted a deal to transfer that legislative authority to Ottawa, turning all the communities therein into citizens of Ottawa's government: without a single consultation with the people.

One of the major reasons HBC was willing to give up their authority was that the major stakeholders (the ones who were getting the payoff from Ottawa) were already knee-deep in industrial investment, and this shift in economic order would serve the expansion of their capital and allow them to get in on the ground floor in a new territory of industrial development. The biggest bribe of all was stakes in the burgeoning Canadian Pacific Railway, which required cession of the land to Ottawa to expand, and promised massive returns once completed. This paid off, as can be seen in the makeup of the MacDonald government, whose ranks were replete with CPR stakeholders.

There were those within HBC who weren't bought off: those factors of the company that weren't privileged in industrial deals and who would lose out when the seat of power shifted to Ottawa. These were the actual fur traders who had a vested interest in seeing HBC retain exclusive ownership of the land. They were the main economic factors backing the Rebellion. Mactavish (who was governor of Assiniboia, and a stakeholder in HBC) was one of the main "canadian" opponents of Ottawa's assertion of constitutional authority over the Northwest, but like a lot of the settlers who were opposed to the annexation (and make no mistake, it was an annexation in which Ottawa sent troops to be permanently stationed and enforce their new ownership and legislative power over Rupert's Land) he largely moved to position the Métis as the main "Rebellion," supporting them privately but in a way where he could deny culpability if the Rebellion failed and throw them under the bus, and publicly supporting Ottawa. He almost certainly intended to subjugate the rebels if they had succeeded and secure power for himself.

McDougall was appointed governor, and he arrived with troops in the mode of a classical British colonial governor, arriving with expectations of a complete pacification of the population. When he arrived, however, he was met outside the colony by Indigenous warrior Ambroise Lepine, with a gun in hand an order to stay out of Red River. This is regarded sometimes as the real "start" of the Rebellion.

The Métis of course were fully aware of little how they could trust their so-called settler allies. They were in no way dupes, and while they accepted arms and funds from the settlers (and in some actions worked alongside them), their Rebellion was an independent political movement with distinct aims. They saw Ottawa's annexation of the Northwest as the continuation of the same colonial structures that had previously pitted them against the HBC, and so while they and the settlers agreed on a desire to keep Ottawa out, their ultimate goal was to set up their own constitution, and they even expressed a willingness to negotiate entrance into Confederation so long as they were granted their full and equal rights and autonomy. This inter-colonial conflict for them was a chance to establish a system of governance that put the people in charge and throw off the rule of the HBC and Ottawa both.

In 1869 the population of Red River had 10 000 Métis (the majority of them, about 6000, of French descent), more than 1000 Indigenous people, and only 1500 white people. The Métis were adamant that they should have control over their own land and resources.

The Métis National Council mobilized the French Métis, prevented McDougall from entering Assiniboia, stripped Mactavish of authority (according to Mactavish, though it's possible he simply said this to not be held responsible for their insurrection, which he himself had encouraged), and then on the 6th of December they occupied Fort Garry, the surrounding area, and Mactavish's own residence. There they issued a "Declaration of the People of Rupert's Land and the North West."

"1. When people have no government, they are free to adopt one form of government, in preference to another, to give or to refuse allegiance to what is proposed. 2. The Hudson’s Bay Company having abandoned the people, without their consent, to a “foreign power,” the people are free to establish a provisional government and “hold it to be the only and lawful authority now in existence in Rupert’s Land and the Northwest, which claims the obedience and respect of the people.” 3. The provisional government would “enter into such negotiations with the Canadian Government as may be favourable for the good government and prosperity of this people.”

McDougall responded by appointing Colonel Dennis lieutenant governor, and ordering him as a "preserver of peace" to begin firing on Métis people (literally any and all Métis people), driving them from their homes, and seizing all their property. The violence against Métis was largely carried out by Orangemen from Ontario (and if you look into the history of Orangemen in Canada you'll see how much of the colonial violence they were directly involved in and how much of the formation of the centralized Ottawa government was built by Orangemen with Orangemen in most of the positions of power.

The Métis then set up a provisional government in January of 1970, with the goal of presenting a unified front to demand autonomous administrative control of the lands and resources of the North West. In February the provisional government issued their List of Rights.

"The Northwest would enter Confederation as a province with the same rights as the other provinces. This province would be governed by a lieutenant-governor, a senate, and a legislature that would be elected. There would be two representatives in the Senate in Ottawa, and four representatives in the House of Commons. This province would not be liable for any part of the public debt of the federal government. All properties, rights, and privileges presently held by the Northwest people would be respected by the federal government. There would be no direct taxation for the first five years. The local legislature would determine the qualifications of the Members of Parliament. The transfer of the Hudson’s Bay to Canada would be withheld where it interfered with the people’s rights. The local legislature would have full control over public lands of the Northwest. Indian treaties would be made between the federal government and the Indian tribes. The cost of all public buildings, bridges, roads, and public works would be paid by the federal government. Both French and English would be official languages. All debts contracted by the provisional government in consequence of the illegal measures adopted by federal officials to bring about a civil war would be paid by the Dominion treasury."

There's a lot more to be said about the annexation that followed, the way the Rebellion was twice betrayed, the way the leaders were set up in a kangaroo court. Canadian history has taught the whole thing in a completely ahistorical manner, as with most Indigenous movements. It's worth noting that many explicitly socialist movements in Indigenous communities that followed upheld the Rebellion, but it wouldn't be accurate to say the Rebels considered themselves socialist. What they did consider themselves, though, is a mass movement of oppressed peoples who believed in democratic control of land and resources in the face of capitalist expansion, and who wanted to ensure the ownership of the North West would be a common ownership of the people, Métis and Indigenous, and not subservient to colonial Ottawa (or the HBC it was usurping).

I recommend Howard Adams' Prison of Grass: Canada From a Native Point of View. Adams was a Métis socialist whose great grandfather, Maxime Lepine, was a lieutenant in Riel's Rebellion.