Most people on here will tell you they can't handle frost. The buttons you have in the US might be lees hardy than the ones we have in Scandinavia, so I won't tell you these people are downright wrong, but I will tell you that mine fare well outside in the winter. I have a group in an unheated bilding and another in an outdoor aviary that is covered on all sides except for the door in the winter. Temperatures of 14 F are not uncommon and occasionally the temp might just drop into the negative F's. If your winters are colder than that, I don't know if they can handle it.
In general I wouldn't mix them with coturnix. The coturnix are much bigger and could easily beat buttons to a pulp. Some people do keep them together - and some do it for a while with no issue, then suddenly one of the cots won't stand the buttons anymore.