The supersoaker and warm water idea was recently posted somewhere else, maybe Ambient.
Where's your water heater in relation to the unit? (Or a laundry sink with the right faucet set with hose threads on the spigot.) If you have a long enough hose, hook up to the drain valve on the tank and blast the ice off with hot water. Just drain the hose afterward so it doesn't freeze.
Or, get some windshield washer nozzles, a windshield washer pump and something to power it, and some aquarium tubing and tees. Affix the nozzles to anemometer. Run the tube down the mast. With any luck, it's on your house and you can run the tubing inside.
Hook up the pump. Whenever you need to deice, heat a jug of washer fluid in the microwave, drop the pump tube in, and fire up the pump.
Or make a cheap hairdryer weatherproof, and mount it up there on an extension cord and plug it in when it freezes.
Or, strap a 1.5" or 2" plastic pipe to the mast and feed the hot air up it as needed. Might have to make a ring diffuser at the top to heat the circumference.
Or (this one might actually work
) wrap the non rotating parts of the unit with heat tape for gutters, run the cable down the mast, and plug it in as necessary. I used to have some cut-it-to-length heat tape that was resistive across the core that would have been perfect for this.
