Interesting question. The L in LCD is for liquid. I'd think that means frozen is broken. But a quick search of LCD repair turns up several DIY solutions. Maybe one will work for you.
lcd are normally good to -50 c before damage. -58f
They will get to a point where they wont read, un readable, become extremely slow, or seem inoperative. Once the weather warms you should be ok. I am in the north east an have seen lcds on bat chargers, and stuff seem to stop working in the cold. I have never had one damaged by the cold that needed replacement .