Yesterday after a days ride my mother's sled wouldn't shut off. She turned the key & nothing happened. Then the kill switch, same thing the sled kept idling. My father pulled the plug wires off to stop it.

This morning he started the sled twice, had it running & was able to turn the sled off w/ the key.

Is it possible moisture got into both switches & caused problems? There was some powder snow on the trail & it was snowing.

Snowmobiles have a very simple system for "on" or "off." Basically, "off" means the engine's ignition is grounded. The Polaris system is quite simple and usually very reliable. Ther are two switches in the throttle, one of which must stay open at all times or the engine will be grounded. Then there is the handle bar switch and, finally, the key switch. Turning any of them "on" opens the ground.

Since your (mother's) problem was the reverse, it is unlikely that the both switches are at fault. Instead the problem is likely in the single black wire which "provides" the grounding opportunity to the engine. It connects at a single wire connecter to a single black wire from the CDI. I would start there and make sure that connecter is securely connected (and free of interference, like corrosion.) If that is okay, then you need to start looking at the condition of wires to make sure they are solid. There should also be a plug on the upper end of the harness which could be the problem.