Most pics I've seen of cold weather damage to flooring was of sheet vinyl- especially if it runs under cabinets it can shrink and tear in very cold weather. Dunno if it gets that cold where you are, but even if it does I'd think that the risk of this type of damage would be greatly reduced with individual tiles. Not to mention much easier to repair if it did!
The one thing I'd be concerned about in this case would be WHY it has peel-and-stick tiles. If that's the way it came, that's one thing. But if it's a repair/retrofit I'd sure want to know just what happened to necessitate the change. Who knows what could be under there, know what I mean?