I live in Texas so I cannot assist you on the ice dam.
However, I had some bad experiences with my last roofing job that now really irritates me.
The insurance agent assessed my roof and I too had hail damage, I had two layers of roofing on so you cannot add another and I had to have all stripped off to the decking. The agent walked the roof and felt that my decking was OK. I also was getting new turbines, wind driven, new stacks, new roof edging, and new gutters with the deal. This is normal because when removing the roof, the old gutters and roof edging is damaged beyond repair anyway.
I got two bids and then went with the one that would come within my allowance. It was understood that IF the decking needed replacing in areas that it would be done and that the agent would agree to add more to the deal to cover that expense.
I was working those three days and when I returned to look at the job it looked nice and neat.
I then walked up into the attic area and found four areas where the decking had actually bowed in and needed repairing but did not. I refused to hand over the check until the decking was fixed. The owner "talked" me into shoring up the decking from under the roof using supports and scabing. I agreed to this, very reluctantly, because I knew the alternative was to remove the new comp shingles and repair the four areas. This shoring was done and to this day I kick myself for allowing it to happen.
So, my point is to be there to self inspect the decking before the tar paper is rolled on. Decking is covered and in many cases it needs to be repaired/replaced in some areas.
Now, if you have only one layer of shingles on your home now, you do not have to worry because the second layer goes on top of this one. But if you are a strip down, watch the decking, the walking, scraping, and bundle dropping with harm the deck.
Make sure the gutters, drip edging, turbines, and stacks are with in the package and you do not have to pay for them. Make sure that you get a thorough magnetic nail pickup after the job. If not you will be picking up roofing nails for years to come.
Make sure the comp shingles are hand nailed, not air driven and make sure 4 nails are used. Allot of companies use air driven nails, and only use three nails. If you do not demand this, and watch this, they will do what they want because you will never know once the roof is on.