Living in an old farmhouse, ice dams are often a problem.

I haven't seen ice damage the shingles directly; rather, the worry is that water will sit on the shingles above the dam rather than draining off. And when water sits, it will find the most minute pinholes, ultimately rotting out your roof.

In the past, I have been observed with a deliberately-dulled hatchet, on a long ladder, chopping channels in the ice dams every 18" or so to make the water drain downward instead of building up.

I think heat tape, turned on for an afternoon here and there, would do the same thing -- creating drainage channels to avert water damage.

I substantially increased the insulation in my attic eaves a few years ago. That reduced the problem substantially. Now, when the weather starts to warm up (freeze-thaw weather), I use an enormously long roof rake to peel off as much snow as I can; then I let the sun do the work of loosening the ice, and come back later with the roof rake to peel most of it off. I haven't been up with the hatchet for years.