The concern about extension cords is a valid one. Very, very valid. The wiring in most homes is either 12ga or 14ga wire, for 20a or 15a circuits, respectively (though some folks put 15a breakers on 12ga wire to be extra safe, and some folks put 20a breakers on 14ga wire because they're stoopid -- point being that you can't necessarily *know* whether you've got 12ga or 14ga house wire by looking at the circuits).
What happens when you run A/C appliances over long distances (either through extension cords, or simply because a house is wired poorly) is that you get a voltage drop....most appliances are designed to run on 115 volts, but at a long distance from the breaker box, you may get significantly less than that.
That's what causes appliances to 'die' young.
The other problem -- the one I'd be most concerned with in this situation -- is that if you run appliances which pull lots of amperage (and a stock tank de-icer is a good example!!) through long, thin extension cords (anything less than 12ga, really...most common extension cords are 16ga or maaaaaaaybe 14ga), the wires will begin to heat up.
When the wires heat up, they can either burn in half and begin to 'arc' (an arc being an open flame, basically) or melt the insulation off and begin to arc, or simply heat up enough to melt the insulation and the wires will set a nearby combustible item on fire.
IF YOU MUST run an extension cord to a de-icer, move the tank as close to a GFCI outdoor outlet on the house as you possibly can, and run the shortest heavy-duty cord (like, a 12ga cord!) possible.
We have a tank de-icer on an extension cord. It's a heavy cord, and the tank's a short distance from the house.. The outlet it runs on is a GFCI circuit, and it's not very far from the breaker.
Still, when it snows, snow won't stick to the extension cord. The cord is warm enough from the draw of the de-icer that it melts snow.
Obviously, NOT IDEAL.
I have plans to run an aerial power-company-sized dropline from a 60A circuit off my main house panel to a 60A grounded subpanel in the barn, from which I'll run short 12ga GFCI circuits. I already have the wire and a utility pole...just gotta set the pole and figure out what circuits to combine in my house, since the electrician seems to have run a seperate 12ga wire to EVERYTHING in my house and filled up the entire panel..

:/
But, seriously...if you're going to run an exension cord, THINK ABOUT IT REALLY, REALLY HARD FIRST.