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Well, there are some heated soccer fields to get rid of snow. Some here in the USA and Canada heat their drive way to do the same. Feasible - yes. Economical - depends on energy prices and how honestly those prices are determined.
Snow ploughs are the most economical way to clear runways where there is regular snow, as they'll be in frequent use. It makes less economical sense to have lots of snow ploughs in places where snow is infrequent as they'll just be sitting idle most of the time. As many of the problems associated with this sort of machinery are not just due to wear but due to deterioration over time, stuff can stop working and need repair even if it's not used.
Black tarred runways, and concrete ones too, store heat and can melt the thin initial layers of snow. To clear the runway of snow will need a lot of power, enough to melt 1km of ice that is 20m wide per runway. That sort of heater is a little bit bigger than the kettle or toaster, and would probably bring down the local grid when it is turned on. Snow plows and salt spreaders will be more appropriate, although no airline will want to land on a runway coated with a lovely corrosive salt layer - planes cost a little bit more than a Fiesta, or even a Bugatti, and salt corrodes alloy rather rapidly. The last thing you want is a panel thinking it is made of "House Brand" foil when it is all that separates you from Sir Isaac Newton's apple.As to the costs of keeping dedicated equipment, almost all airports have at least one front end loader, for general use and such, which can be used as a snow plough for those airports without dedicated snow clearing equipment. A bigger issue is that the aircraft themselves will require de-icing before takeoff, which does need specialist machinery, chemicals and trained staff ( Most important) so that a layer of ice does not spoil the flight capacity of the plane.
"I'm going to through my knickers"Seems like the snow has FOGGED your brain sheepy.
The only practical solution I can see is to build an airfield and nuclear power station in close proximity with provision to divert some of the waste heat from the cooling towers to the runway.Unfortunately both runways and power stations are very unpopular with the local people so there might be problems getting them built.