Extend the vent out away from the house.

This is hard to believe. Do you have pictures?

I agree with ionized. How do you know the problem is your dryer vent? Are you just assuming or have you actually stopped using your dryer and the problem went away? It seems to me that the air would be cooled long before it reached your overhang.

Are you sure there isn't just a problem with your insulation in the attic?

It does sound unlikely - is the vent pointing upwards?

It does seem to be a long way away from the vent. Mine points down, and clears the snow and ice for a couple of feet around, but that's it. No icicles.

I have to agree, it sounds like a coincidence. Check for missing insulation, uninsulated exhaust fan ducts or heat ducts running through that part of the ceiling.