#s would help tell if it till has points or is electronic ignition. What may be helpful is to take a spray bottle and direct the water spray into areas which may indicate where the issue is. Start the engine and spray the spark plug, then the plug wire, maybe even kill wires. It isn't a common problem, but if a coil were cracked or the cover not installed on the points- that would be best guesses. If you were careful and had electric start, one could remove the recoil blower housing to expose the coil. Start w/ the e start and try the water treatment. Just run the engine long enough to do your tests to prevent overheating. If the engine is old enough for points, 20 years old? they are under the flywheel.

I suspect the spark plug wire has gone bad and needs to be replaced.

When its cooled off, spray WD 40 on the wire.

See if it stops running next time we get a snow storm

The sparkplug wire has indeed "dried out" and needs to be recoated to keep it waterproof,when the snow mist hit the wire it's shorting the electrical to ground and killing the engine.....The cheapest fix is to remove the recoil cover and spray the sparkplug wire with wire dry and then recoat the wire with plasti-coat for ignition wires....these two items should be available at any auto parts store ....Good Luck ,Jim

Ages ago, I coated the the wires on an old Willys with di-electric boot grease. It worked great.