You're on the right track, but it's simpler than that: Your engine at idle produces a fixed torque. Shifting to a higher gear reduces the torque applied to the wheels. If the torque at your wheels is great enough to overcome the static coefficient of friction, then the tires slip, so less torque is better.
Of course, the clutch does come into play. Since the engine wants to stall if you start out in a higher gear, you naturally have to let it slip a bit as you're starting out, which further reduces torque at the wheels.
The "Cruise-O-Matic" transmissions in the Fords of the mid-sixties had a shift position specifically for starting out in slippery conditions. All it did was lock the transmission out of first gear.
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Today's Featured Article - Good As New - by Bill Goodwin. In the summer of 1995, my father, Russ Goodwin, and I acquired the 1945 Farmall B that my grandfather used as an overseer on a farm in Waynesboro, Georgia. After my grandfather’s death in 1955, J.P. Rollins, son of the landowner, used the tractor. In the winter 1985, while in his possession the engine block cracked and was unrepairable. He had told my father
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