Your concerns are justified. First without drainage holes in the bottom, there may be root rot and other problems.  Containers without drainage are not recommended for plants of any type.

Second, there must be at least 8-12” on each side of the plant to even consider overwintering outside. If you look at plantings in commercial areas in containers that over winter, they often are concrete which is better insulator than metal and more than two feet deep.  

Some shrubs can be overwintered in very large pots with drainage holes and wrapped with insulating materials. I do overwinter pots in a garage which moderates the temperature. I also successfully sink plants in containers into the ground for winter protection.

The following websites have additional information:

1. https://gardenmaking.com/overwinter-perennials-in-pots/

2.  https://www.provenwinners.com/overwintering-perennials-shrubs

3. https://www.bbg.org/gardening/article/overwintering_potted_plants