How cold was it and how much did the furnace need to run? How much power does your furnace require?
An extremely rough rule of thumb is that a battery is good for a night's furnace usage, but there are so many variables it's hard to be at all precise about things without more information. It could very well be that your existing battery was on its last legs to begin with. It also could be that you need more battery power to reasonably get through a cold night's furnace usage. Rather obviously, turning the thermostat down during the night will reduce the furnace run time and economize on battery (and propane) usage.
If you have room (height, mainly) for them, a pair of 6V golf cart batteries (wired in series) will typically give you more usable battery power than a pair of 12V "deep cycle" marine/RV batteries in parallel. They're also more robust against the occasional deep discharge.