My wife uses a bottle like that, because she doesn't want to drink from plastic bottles. (I don't blame her.) She uses a cage with a rubber strap that opens on the side, because her top tube is so close to the down tube. It works well for her.

The stainless steel is likely to hold heat better than plastic, but there's no way to say if it will be enough. Being out there on the frame out in the cold makes it unlikely. You might want to store it in a warmer but less convenient place.