Does snow on the roof help or hurt my heating bill?
Yes, it does. It also shows that you are not losing heat and that you are well insulated.
I would think that the snow on your roof actually helps to insulate your house more. Think about dog sled teams in the far north the dogs dig themselves under the snow to stay warm at night. Also I have taken winter survival trips while I was in Canada and was taught that snow acts as an insulator. I think it helps.
I mostly shows that your home is well insulated and not loosing heat through the ceiling to melt it. Think of an Igloo made of packed snow. It can be kept at a temperature just below freezing so that it will not melt and still keep those inside from the 30-60 below outside.
It shouldn't matter. Here's why: If your attic is already well insulated and ventilated, there is insulation sitting on top of your drywall or plaster ceiling. Above that insulation is moving cold air. That air keeps your roof from rotting. The insulation creates a barrier between your living space and the moving air in the attic. You can differentiate homes with good insualtion from those without it--well insulated homes will have snow on their rooftops for a longer time. Additionally, well insulated homes are less likely to develop ice dams. So, I don't believe the snow on your roof should make any difference at all in your energy bill.
To building professionals, it means you are properly insulated. It does help a bit, in that without it, you'd be exposed to cold winds, which are worse in removing heat from the house. Typically, we like to see (and count on) some snow in how we design houses and size the structural elements of the house & roof. If you are talking over about 3', though, we might be getting nervous about the weight. Each city/area requires that we deal with normal snow loads of that area. But 3' deep means there's about 180 pounds per sq foot of weight on your roof. About that point, I get up there and remove most of it (I leave about 12" thick). Still same on the thermal characteristics but safer on structural. .
