Edit: We survived an ice age and we're very highly adaptable. Plus, we will hold on to some percentage of technical knowledge that will help us adapt faster.
I like your optimism, but I don't share it. We honestly don't know, one way or the other. What we do know is that human extinction in on the table and growing in probability. When I look at human actions as our cumulative knowlegde of these risks grew, well, I'm not exactly confident our species will make it.