Can trees live long, healthy lives in a pot?

I live in San Francisco and I’m fortunate enough to have a little yard. When I purchased the house, it was nicely landscaped. I have three little dogs that have killed practically everything in it. I want to have plants and maybe a couple of trees, so I thought keeping them in oversized pots away from the dogs would solve the problem, but will trees and other plants fair well in such containers?