From the description, the relays should take up to 120v, but it isn't safe to work at that voltage. The voltage regulator on the board, a 7805, should be fine up to around 20v, but since it's a
linear regulatory, it would get very hot at that input voltage. You should be fine connecting it directly to your car's battery/a cigarette lighter port on your car/etc. The most you'll probably ever see at your cigarette lighter is around 13v.
Don't forget to put a fuse on the power line coming from your car. If something shorts you want the fuse to blow instead of something catching on fire.
Lead acid batteries are prone to
thermal runaway when shorted. Higher temperatures decrease the internal battery resistance causing more current, causing more heat... That's the same reason it's harder to start a car in cold weather, the battery's internal resistance is higher when it's cold.
Encryptic is right to suggest waiting to see if you hear from someone experienced with AVR programming. You might also ask for help in the AVR forum here.