Peel & stick tile manufacturers warn against usage in temps below 55 degrees.
Having said that I replaced worn vinyl with them in a 1984 Prowler many years ago.
It survived four Canadian winters with no apparent effect before I sold it.
Last winter (which was brutal in Michigan) tore the vinyl in my current fiver - you could see where it had shrunk, pulling out from under the cabinets and around the floor vents.
I removed the sheet back to the bare plywood and have installed Armstrong P&S tiles over it.
Time will tell how well they will survive.