That's one of the (many) cruel truths of thermodynamics. It doesn't matter
how you apply the energy, it takes the same amount of energy to melt or vaporize something. The only place you can really gain is in efficiency, which I suspect in this case mainly takes the form of how much time you spend heating up things other than snow. And, sadly, I don't think ultrasonic is going to be a huge efficiency boost. In fact, those humidifiers and air fresheners cheat horribly by not actually melting, boiling, or vaporizing anything at all. They just splash the liquids around
really hard when they hit the rapidly-moving diaphragm, and create a very fine mist of droplets
Water is also surprisingly hard to melt. Both its specific heat capacity (energy required to raise its temperature) and its enthalpy of fusion (energy to change phase to liquid) are quite high compared to other common substances. Assuming I'm not horribly misapplying the calculations here (which is entirely possible), a
mere 100 kg of ice would take
5 hours to melt using the full energy from a standard household 15-amp electrical circuit, and that's if you don't waste any of it making noise, light, magnetic fields, or heating anything other than the snow.
All of this is just a really depressing and detailed way of saying "there's a reason we don't all use radiant heating systems to keep our driveways clear." Although I have read about such systems being installed by the very wealthy, using closed loop hot water circulation. And there's a stripe all the way along Iowa State's campus where an underground steam conduit used for heating some of the older buildings also prevents snow accumulation. But that thing is directly fed by a coal-burning cogeneration plant, capable of producing 900,000 lbs of steam per hour, so it's not subject to quite the same limitations as most households.
Having said all that, I am very interested to see what you can come up with.