How is the temperature on your fridge being controlled? If you use a two stage controller, you can add a small heating element (light bulb even would be enough) to keep the temperature inside the fridge at your desired temperature. Converting electricity into warmth is much easier than converting electricity into cold.
As for the poppet, it's tough to say without seeing it. I can imagine that the freezing simply hoisted the valve open, but it's also possible that there was some more substantial damage. Test it out...if it still holds pressure, I'd wager it's fine.