Do long roof overhangs influence ice dam formation?
Longer overhangs could impact ice dam formation, but it does not seem to be a significant factor. As this page from the University of Minnesota outlines, heat loss through the roof is the big contributing factor. They even go further and say that air leakages around light fixtures and such on the ceiling of the top story are the biggest culprits. Nowhere on that page is the size of the roof eaves even mentioned.

Longer eaves could increase the size of the ice dams, possibly preventing or delaying damage to the structure of the house. Or the water may freeze before it reaches the edge of the roof, as if the eaves were shorter. It probably depends on the temperature differential on the roof and how cold it is outside.

In any case, icicles are a sign of heat loss through the roof, and corrective action is advised. It may be as simple as adding insulation in the attic, but may involve sealing up areas around light fixtures, moving exhaust ducts (e.g., driers), using fireplaces less, etc.