Tony

"I think that would be the right thing to do as well, but shouldn't a mimosa tree be able to stay outside all year around if it had to?"

Yes they can stay outside in the winter. They're not quite as cold hardy as the others I mentioned. It would be a good idea to dig these into the ground and set them on bricks to keep them out of any water that collects. Then you can place mulch over the pot and all, up to the first branch. The ground will keep the roots a bit warmer than otherwise. Even though a certain tree may be hardy to your area when grown in the ground it may not be when grown in a pot. It's a whole bunch colder above ground. Any questionable trees should be given added protection like above.

Tony