concerning the insurance company. This should have been done with the detection of the first drop of water. Take pictures and document the extent of the damage and have an agent or adjuster see everything.
Now, there is so much you can do to minimize the damage in the home interior. I would cut away all the wet ceiling and wall material and let it start drying or airing out. Drywall conducts water by osmosis or by soaking to the ajoining areas. Get fans going and keep the water pails out.
If it was my house and I was in the situation, I would be up on that roof with tarps and stuff to minimize the leaking into the home. There is so much you can do to keep things in check until Spring. Tarps, tar paper, plywood and the sorts.
Get some assistance and do some damage control work and get the insurance company on it now and homes are roofed all the time during this time of year.