If you can't remove the chain to thoroughly clean it, try to dry it off and then brush off as much grit as you can before you re-lube. That's my biggest complaint with wet riding--my chain acts like a grit magnet.

Removing the chain to clean it is sooooo much easier than trying to do it on the bike. If you plan on riding in wet weather frequently, I'd recommend spending $15 on a Wipppermann link or some other removable chain link. You'll save a lot of time and your drivetrain will last a lot longer if it's kept properly cleaned and lubed.