You can't run the carb out of fuel, the bowl will always contain fuel even after the engine dies. You must drain the fuel bowl, treat the gas, or let it be. On smaller engines there should be a screw or the bowl is removeable. If niether are an option, put some HEET or other gas treatment in the last tank for the last trip of the year. I run Seafoam in all tanks, plus I run 10% ethanol. The ethanol and Seafoam clean all the varnish gasoline leaves behind.
Also pull the plugs (clean and gap, or replace) and spray WD-40 into the chamber. It'll leave a protective coating, and will burn off in the spring. WD-40 stands for Water Displacement 40th attempt.
I prefer to empty the gas tank and leave it dry over winter. If you cant empty the gas tank completely, then its best to top it off. More fuel, less water condensation and the less internal rusting, if your tank is metal, add a fuel treatment.
Come spring I'll fill up with fresh gas (10% ethaonl)/oil and add seafoam.
Charge the battery.
Pull the plugs and clean or replace, spray some ether, and put the plug back in.
Fire it up in a barrel and let it run for a bit, then take a 1/2hr. cruise around the lake.
I do the same thing with my riding mower, and weedwhacker.
On the rider I'll change the oil and filter in the spring, sharpen the blades, check tire pressure, etc. Plus clean the air filter, clean the deck, etc.
I do plan on replacing the head gasket, reeds, and may soak the carb while I have it off this winter. Thinking I'm only getting power from one of my pistons.