My Suburban furnace pulls 2.9 amps and my propane detector pulls .046 amps per hour. The blower motor in the furnace pulls more than I thought it would; took me a while to find out exactly how much without a meter.
As has been mentioned, some battery manufacturers label their batteries at a certain amp hour rating at a low discharge rate like 1 amp hour. This is misleading to the consumer.
Batteries will indicate a lower voltage in cold weather so this many be why your alarm is going off. I would test it again using a multimeter in warmer day temps (unless you are stuck in the polar vortex!)
I have found for myself that this is the reason that I need to know exactly how much power everything uses. I have a small solar system with a four year old, 100 a/h, C-20 Lifeline battery. The high summer temps here really hurt the battery. It's almost time for a new one.