My mother has been growing the same mint in plastic urn containers for who knows how many years. She sometimes sticks the containers under her open but covered patio and every year they resprout. She got some chocolate mint from one of my sisters last year and it resprouted and has filled their container so far this season. I would say her urns would be like 10" pots on a little stand. I have some in a wooden trough on my balcony that occasionally some peppermint that I planted a bunch of years ago pops up.

It hasn't hit 0° F or below here since 1994 so I'm not sure what would happen to them but we have had a bunch of days in the single digits for sure and they have done okay.

Note that the mint that she is growing is mostly spearmint or peppermint and those are a bit hardier than other mints. You want to check for the hardiness of the mints that you want to grow and then subtract 1 - 2 zones from your own zone to estimate the coldest type that you could put in a container without protection. If you put the container in a garage, then you should be okay in any case (except for perhaps the very tender ones if the garage is unheated).

My opinion is that you should only grow it in a pot becasue it can be very invasive. At least around here that is.

We usually get sub zero temps here in Chicago. My experience is that spearmint has been the least hardy in containers. Apple mint and peppermint are average. Chocolate and cat mint seem to be the most hardy. This year we had a very cold Spring and I lost all my mints except for one container which was big. The nice thing about mints is you can easily propagate them. I almost lost two containers of chives this year too which are almost impossible to kill off and I lost all my oregeno which always came back from previous years.

I've grown catnip in containers for years.
The containers range in size from 12" wide x 10" deep to 5 gallon buckets.
I believe catnip is in the mint family.

-hydropetunia

I'll mention too that I have tried a couple times to keep bee balm, which is a mint (Mondarda didyma "Jacob Cline") going through the winter in a 1ft x 2ft trough for the past 2 years and considering how hardy it supposedly is, it's been a no-go. I'm trying a different cultivar this year - "Gardenview Scarlet" (couldn't find instant Jacob Cline) and will see how that does. Even though JC was supposedly one of the most mildew-resistant, it still got it (not as bad last year though) and am wondering if that just weakened the plant. I also have an Agastache rupestris (also a mint) in a container and that I brought in this past winter as it is still a relatively small plant. It's back outside growing and hopefully will bloom soon.

Im in Ohio and learned the hard way to ONLY plant spearmint in containers :) holy toad! I was unfamiliar with mint, thought it was so green and pretty...I planted it around my reflecting pond, soon I couldnt SEE the pond! Took me a year and a half to eradicate it but now I have two nice sized containers with lots of mint for my tea. I bring the containers into my closed in porch in the winter and they do fine.