I researched this a lot myself - if you Google it you'll find all sorts of information online, including instructions, guides on pipe spacing and depth, how many / long / kind of loops you need, etc. I backed off. The consensus was it takes an enormous amount of energy - like, my boiler puts out 125kBTU/hr and heats my house fine, but a calculator I found said I'd need like 2 MILLION BTUs to melt 8" of snow off a driveway with my dimensions. That's a 16-hour burn without even giving the house any heat.
It seems like the trouble is the depth. Anything can melt an inch of snow - I don't even shovel that much, just drive over it. But to melt 6-12" you really need to pour on the BTUs. It's a linear relationship with depth. 6" is like six 1" snowstorms in terms of the heat you need it. It's not like once it gets melting it stays going - as @
hupte pointed out above, it can turn back to ice really easy if it doesn't melt enough to flow all the way off your driveway. And let's not forget what the plow is going to do to the end by the road...
I concluded that the amount of wood it would use wasn't justified. It's cheaper to have it plowed than to buy that much cut/split, and if you get your firewood for free, it's still faster to snowblow yourself than to cut/split enough wood to melt it.
Put another way: if I had the kind of coin to not care about the math, I probably wouldn't be heating with wood.