Not likly any insurance companys going to pay for a lack of maintance issue. They would have if it was wind damage or if a tree limb fell through it.
When buying, inspecting or getting ready to remodel any home the first thing I look at is the roof and all the flashing, plus the morter around a chimmney.
If the roofs not tight then anything you work on below it is trash. The last thing someone should be doing is trying to replace a whole roof in the middle of winter. The shingles will not get hot enough to seal down. I think I would for now just work on the one area where it's leaking and save the rest for spring or summer.
Since you let it leak so long there's most likly going to also some roof sheathing thats going to need replacing. If the inulation in the attic is wet remove it and trash it asap before mold sets in.
Ice dams are caused from lack of insulation in the attic and not having a heat strip inside the gutter that runs down the down spout.