Patton probably died at the absolutely most perfect time. He would have hated peacetime and he probably would have been frozen out of any meaningful role in Korea by Dugout Doug.
It's hard to say and would depend on politics and intra-Army maneuvering. He'd initially be a big player in post-war occupation, might be ready to lead an attack to reach Berlin in the Berlin crisis, and would ensure US troops dealt with the both the occupation and any Soviet aggression. While he might have lobbied to fight in Korea, the Army (notably McArthur) might have kept him out of it.