I've got four pawpaws growing happily on my property near the north shore of Lake Ontario. The only real winter damage they've gotten was when the fence fell on one of them and broke it at knee height. Ugh. But that one is currently pushing out a new leader and lots of leaves.
Some are in full sun and some have noon shade from our big old black walnut. All seem happy. (I understand they don't give a fig - pun intended - about juglone and are a great companion plant for black walnuts.)
If you're buying, I'd go potted over bare-root, hands down. The first two pawpaws I bought were bare-root and they struggled all year and then died the next spring.
The second pair I bought were bare root and they struggled the first year. One took off in the second year (only to be crushed by the fence) while the other died back, but has since sprouted like nobody's business from the roots. They're the native Ontario variety - there are wild pawpaw patches in the Toronto area and southward, but they're exceedingly hard to find as most of their native range has been bulldozed - and I'm assured that they'll a) taste great, and b) grow like stink once they're settled in.
The ones I bought potted, meanwhile, have flourished. I know I'm pushing the Peterson Susquehanna variety here (if I'm right, they'll ripen for me just before early frost risk, around Canadian Thanksgiving), but it's the best grower out of them all (though it leafs out a bit later). It's taken -20C without any damage. No flowers yet. The other one I bought potted is an NC-1, and though it grows a bit more slowly than the Susquehanna, it's the only one yet flowering - at about 3 years of age! It pushes out leaves first out of all of mine, with the native ones a few days behind, and the Susquehanna a few days behind that.