Well the mere fact it runs is a true testament to how well Honda builds things.
It has most likely sucked some water into the carby. Drain the fuel out the bottom of the carby into a container and check to see if it is contaminated with water. that goes for your fuel tank also.
The carby should have a hex head plug at its base or a drain scew outlet. Failing that, take off the float bowl. Be careful when you do that though, If money is an issue, you don't want to wreck the gasket or break any parts.
In regard to your air inlet setup. The hose diameter for that type of engine doesn't look too small, just filter the air going in somehow. If your always going to go swimming with it, mount the hose higher. Lots of Trikes had the air inlet feed from up near the head stem, see if you can rig up something like that. Also put on a pod filter by crikey man.
You may also be having some electrical issues. Squirt water dispersiant (WD40,CRC,INNOX etc..) into the magneto/points pick up area and onto any of the electrical connectors
Oh, and get the seat recovered you slack arse and have a bloody haircut!
P.S. good luck with it.
My toys 85 KXT250A2, 85 ATC250R, 85 Tri-z 250, 06 LT-R450, 04 YFZ450S, 07 125 typhoon x 3, 06 FPV GT.