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.
Climate change is an ongoing process that takes decades to centuries. That's very fast as far as evolution and natural climactic shifts are concerned, but on a human scale long term. Given that it's not stopping within the lifespan of one person, and contributes to virtually every health problem in subtle ways, it'd seem a bit difficult to say if a given person has "survived it" or not, even if they live to an old age.