Brad, some others with more experience my have better guesses, but it seems to me there are several possible choices.
1. Engine issues, if the engine is running smoothly during his problem then rule this out.
2. Clutch/transmission issues, this is no different than a manual transmission car, under load if you have a transmission problem with a car that has a manual transmission then a jerky ride is not uncommon.
3. Variator/variator belt issues. This seems to be more likely than a chain drive issue. If you had a few teeth knocked off a drive sprocket then you'd be slipping on ONE track, not on both tracks, so the erratic movement would tend to drive the Snow Trac one direction only. The Variator system controls both tracks and should then affect both sides.
Just my thoughts . . . now I need my morning coffee.