Like a lot LCD displays, their response will slow at low temperatures. You may also notice that the display contrast will alter as the temperature changes, making it more difficult to read. The actual temperature at which damage is likely to occur is well below what it will experience in an unheated garage.
I have an external temperature transmitter that has a built in LCD display. it has been outside for the last 2 years, down to about -9 deg C, with no ill effects so far.
It is important that you avoid condensation on the electronics during use, but apart from that, I wouldn’t worry.
Regards,
Anthony