There’s no doubt that climate change will negatively affect most countries in some way, but the question is: do you think Canada will fare better or worse relative to other countries?
I would wager that if future Montreal, for example, had winters more similar to today’s New York, far more people would want to live there.
I can only assume you've not been to either city if you think Montreal is that much worse or NYC that much better, in terms of year-round climate.
But more importantly, you can't increase your population if your cities have to ration the water or food supply because climate change has destroyed both. And mass migration is not going to happen without destroying lives and livelihoods.
I’ve lived in NY and have visited Montreal a bunch of times, including one unfortunate trip in January. The average high in January in NYC is almost 40 degrees, and it’s 25 degrees in Montreal. It is objectively much colder!
I think you are overestimating how much climate change will affect the food and water supply in North America. There will be huge problems but the apocalyptic idea you seem to have is more of a pop culture notion than a scientific one.
I would wager that if future Montreal, for example, had winters more similar to today’s New York, far more people would want to live there.