Not completely true as he is using the energy of the sun to evaporate the water back into the atmosphere so it will snow back down. There is an external source of energy in the system, HOWEVER the odds are the water run off from melted snow would not produce much power at all.
Personally I think it's simpler than that.The power from melted snow dropping the distance of the miners away from the snow determines the power (as the head of the water and it's mass determines the output from the turbines - P=rho x g x h x q), but the heat transfer from the miners to the snow to melt it is inversely proportional to the distance from the snow away from the miners (Qcc = -ci.ρw.hm.(Ts-Tm))
The water evaporating and turning back into snow would only keep the system running if the above could be made to work, but as you'd never get all the heat to the snow perfectly, and rho is always less than 1, you have a slight problem....
As I said, much easier to let the heat of the sun melt the snow and just stick your hydro station and miners downstream from it
Justin
CEO
www.megamine.com