The ATtiny85 can go down to -40C the datasheet says. I'm pretty sure by that temperature the internal resonator will be way off so you better get a decent one. Maybe go barebones there.
Actually i did finish a version of this one, was working great until i went outside. It was so cold outside (like -25 c ) So the trinket actually stopped working until it was back to room temperature. I need to figure out how to keep the trinket warm and still keep it small. Maybe mount it on top of the battery and make some kind of insulation. But still while maintaining the small factor and the possible risk of that my dog is going up in fire