Again, how cold for how long?
For nights in the 30's we have shut the furnace off and used the quilts, in the morning the TT was in the forties when we turned the furnace on. The days were bright and sunny and we were out snowshoeing so the TT stayed in the mid-fifties with no furnace.
I do not think I would go more than a day on my battery, I have found that the phantom loads alone will pull my battery down to where the lights are noticeably dimmer in just 4 or 5 days.
Running off of the battery is for us a unique experience usually when we are in the "camp and go" mode and do not even unhitch for the night. We almost always have shore power and a small space heater.
I do not know why the current through the 7 pin TT plug for the battery is limited; I am told it is more like a trickle charger. Many folks find it easier and faster to charge their TT battery with a set of jumper cables from the TV.
Winter camping is like boon docking or other off the grid adventures, in order to do it you have to know YOUR TT systems and acceptable comfort levels. This is best learned in the back yard.