A crash in fur prices or some other event (A scandal of some kind, perhaps) that would bring down the Hudson Bay and/or Northwest Companies would do wonders to limit British settlement of the Canadian West. If you want the POD to be before WW-I, than its almost essential for Great Britain to see no reason to extend its control of Canada into what they might call "A desolate icebox". A stronger push by Russia or Spain to make their claims to the Pacific Northwest stick, preventing settlement around Victoria (or whatever it would be called in this timeline) Island would also help to keep the Canadians focused on their Atlantic possessions; perhaps leading to a more densely populated eastern Canada. Then its a question of how long before Spanish/Mexicans or Russians decide to peddle off their land to fund concerns closer to home or lose it in an eventual war with the US (Heaven knows both Spain and Russia will need the money at some point to fight this or that war). After that, if the Canadians aren't expanding the Canadian west might well just fall into America's lap.
An earlier, but less likely alternative, could happen as early as the Revolutionary War if the Franco-American alliance manages to take Canada. Even though the American government didn't want France to re-take Quebec, King Louis has enough political and financial leverage over them that he could probably regain France's lost territories in the Treaty of Paris if he set his mind to it or somehow got French Marines into Quebec City and Montreal. Assuming there were any British mainland possessions left, they'd be accessible only by the isolated ports on Hudson Bay, meaning further colonization isn't likely. French Quebec, meanwhile, wouldn't have the population to push west unless they decide to send dissidents/excess population there (A possibility, considering food shortages in France at the time), and assuming the US could eventually acquire Louisiana from Spain they would, again, likely just have the Prairie provinces fall into their lap by default.
In terms of consequences, the "Wild West" and Frontier Era would certainly last longer than it did in our timeline; possibly up into the 1930's. It would also likely maintain more of a "Paul Bunion" feel than the "Home on the Range" spirit we saw in our historical imagination. Lumberjacks in flannel would stand alongside cowboys in their broad-brimmed hats to tame the wilderness, and a romanticized version of fighting the frozen winter being just as iconic as the wide, sunlit deserts. Another factor to consider is public land; if the American West is any example, the Federal Government would likely have come into control of huge swaths of the new territory and could use the sale of that land to fund more projects than it did historically; perhaps we'd eventually see a few hydroelectric dams funded by giving land grants to construction companies in the same way we saw railroads built? The region would probably get most of its immigrants from already established American territories around the Great Lakes; Minnesota, Wisconsin, Michigan and the like, acting to expand "Yankeedom"'s influence both economically and in terms of popular culture.
As for the remainder of Canada, regardless of who it remains under the territory will likely be far more Frenchified than it is today, since the country would remain clustered around the St.Lawrence river and there'd be less motivation for Anglo immigration. Expect French to be more widely spoken in Ontario and the Maritime Provinces than it is today, and the Quebecois influence to dominate the culture. This would likely decrease the perception of similarity and "sister nation"-hood that the US and Canada share in our timeline, as the language, culture, and historical patterns of the two states (Canada would lack a 'frontier phase') would be far more distinct from one another.