Obviously, the further back you go, the less able they would be able to cope.
I'm not sure that's true. People from the recent past have already formed opinions on many subjects of modern interest, like transgenderism. Someone from the 50s would probably be quite bigoted against homosexuals and transgendered people. Someone from ancient Greece not so much, particularly since homosexuality was more accepted then.
A person who has no experience with such things would at least be able to form their own opinions rather than conform to societal norms from their time. The further removed from their time they are, the more adaptable they will be to new social norms. I imagine the same will hold for people frozen now. They'll be able to adapt more readily if they wake up 500 years from now rather than 100 years from now.