As long as you go for small birds - budgies and smaller - your cots should be fine. Cockatiels would probably be fine as well as they are quite mellow, but I don't know how cold hard they are. I'm also not sure what other small birds are cold hardy.
I have button quail, zebra finches and budgies and I have seen the zebras pestering the buttons but with the coturnix being about 4 times bigger than a button I think the zebras would reconsider their position in the hierarchy. I have also seen the budgies running after the buttons, but the buttons run faster and the budgies quickly lost interest. Only real problem was when the buttons had chicks, a budgie caught a chick and nailed it to the ground while examining it with its beak and whereas the chick didn't appear physically hurt, one died the next day and I'm pretty certain it was the one the budgie caught.
Budgies (or budgerigars as they are called) can survive pretty cold weather, but around here it's actually illegal to keep them without access to a frost free room. While not strictly necessary, it is a good idea to do so - it will also keep their water from freezing, making it much easier to care for them during winter.
Pigeons are a good idea as well.