My question regards options in dealing with ice build-up from the furnace exhaust pipe during the winter.

We have a summer home in northern Michigan (Leelanau penninsula) in which we have a high efficiency (90%) forced air furnace. I do not recall the manufacturer, but it was installed by our builder's subcontractor whom we cannot contact (moved out of area).
We have no problems with the furnace.
Our problem is this:
We turn the heat down during the winter to 50 degrees; it saves propane, obviously, but keeps the house at an above-freezing temperature.
The furnace exhausts out the side of the house, and water drips from this pipe, which I am told is normal for a high efficiency furnace. However, when it is cold, the water drips and forms an ice-stalagmite (icicle forming from the ground up).
Our neighbor, in the past, has come over and knocked the icicle away from the pipe, so that it does not ice up over the pipe and cause the furnace to shut off. However, they are moving, and will not have them around this winter to watch the ice for us.

My question is: is there something that we can do to prevent the ice from building up?
I have thought of:
1) heat tape -- but I don't trust leaving a heat tape on, along with an extension cord dangling outside and possibly shorting out and causing a fire. Option 1 -- shot down.
2) extending the pipe -- but to where, and wouldn't the ice just build up inside the pipe, rather than under it; also, the pipe probably is sized in a particular way according to the manufacturer. Option 2 -- shot down.
3) Putting a 5 gallon bucket filled with calcium chloride under the pipe. But....???? Option 3 -- ????

Any ideas out there that would be safe?
We are out in the middle of practically no where, so there are not a lot of people around -- our neighbors were wonderful, but now they're going.

Thanks....