The Low Temperature thing is where the issues will be, mainly due to issues with condensation causing false alarms etc.
If all else fails, a battery-powered home alarm (Garrison, Kidde) is definitely better than nothing.
For under $200, there's ones that are designed to be portable, like this one:
https://a.co/d/a1wBPEd
I think that's what I would get if I would be overnighting on the ice with a heater.