Digital Thermostat Cuts on AC During Freezing Weather

Thanks everyone for the tips.
Cavie: I want to change to an analog thermostat because the digital one is too sensitive. It's mounted in my hallway and every time we walk by we'll somehow change something, Probably just brushing it with our clothes or something. Its gotten to be a major PITA for us. However, since my original post, I've ordered one of those clear plastic thermostat covers and once installed, might just solve our problem.