Sounds like a starter problem to me. I rope pull a 12 horse Techumsa on my splitter. Course the other day at -20 i had to uncouple the pump, start the engine and when it was warm Rebolt the pump and pull again. When the oil was warm it started easy enough. I don't know if a Kohler has splash or pump lubrication. If pump, stiff oil can add to the problem.
Bill