I would be removing the engine on that quad and open it up to get water and mud from every nook and cranny it can hide in.
The amount of water and mud is directly proportional to how fast you want to go riding again.
The likelyhood of it causing you grief is directly proportional to how many shortcuts you took in cleaning it out.
Final drive rear end, if it is shaft driven, can probably be drained then refilled with some cheap thin lubricant and the machine jacked up on blocks and run with no load against the tires to wash the insides, then quickly drained watching to see any more water coming out. When it is clean put the proper lube back in it and it should be okay.
I had to do this to an offroad sidecar machine many years ago after it broke through some ice into about 3 feet of water. After removing the plugs and pumping the kicker, ( I said it was a long time ago ), it started right up and was ridden some miles back to the shop. Whrm I pulled the engine apart, there was green Wateroil foam and silt clogging everything.