I have always drained the fuel in lawn mower and snow blower, then run the engine until it's out of gas. I change oil at beginning of season before starting it, and use fresh gas. I don't really rely on stabil. Not saying that's ideal but I like to drain it.
That is my procedure-I clean the under carriage and the drive wheels also.
I take off the drive wheels and clean them tonly because my father tends to abuse it a bit--Had to replace the transmission assembly a few years back.
Transmission=Front axle driven by the belt-think of it as a rear end in a car.