If the seal is failing that fast something is badly wrong....
Seals fail like that when the shaft is walking around. The end play is excessive, and with tapered roller bearings, this equates to side to side play as well.. .
If it were mine, especially were snow cats go, I think I would ground it until you get a chance to remove it and inspect the innards..
Not that bad of a job on a Tucker I would think. If you wreck the gears in the case, you might be surprised at the $$$ to repair.
Reagrds, Kirk