Container gardens need a bit more care to make it through winter than their in-ground brethren. Keep in mind that the best overwintering practices will depend on the individual plant species.
In general, you should bring small pots into a shed or garage. Cut the foliage back at the end of fall. You can dig up bulb plants and move them somewhere dry, cool, and dark.
Potted perennials also won’t be as hardy as they would be in the ground. Insulate large containers with hay and burlap. Avoid materials that will stop moisture from getting to the potting soil.