As I understand the problem the Ice dam alone isn't really causing the
problem, the problem is with capiallary action which is wicking water
back up under the shingles and attacking the roof sheathing, which is
why more and more "snow shield" a bitch sheet product is being installed
farther south than New England now.
the only ways around this w/ which I'm familiar are a "cold roof" and
electric heat trace cable...

in re gutters- and my yard 18" down is the most beautiful bankrun I've
seen- I believe them to be essentially as useless as chimney caps, I
refuse to get on a ladder anymore to clean out the 2nd story gutters and
fully plan to have them removed the next time I paint