Assume your heater runs half the time and you run it 8 hours a night.
3.4 amps*50% duty cycle*8 hours a night =13.6 amp-hrs per night
You can only drain a battery to 50% without damaging it:
110 amp-hrs*50%= 55 amp-hr usable battery capacity
55amp-hrs/13.6amps/night~4 nights
Don't forget you'll have lights and other loads running which will decrease the battery run time.
Bruce