If the the run they have has a flat top, could you fit a sheet of clear plastic over the top of the run, this would then keep some of the rain off their particular bit of grass. If so move them to a bit of garden you don't mind going bare, together with the plastic they will end up with a bit of bare earth but at least it will be 80% dry and then come the spring you can reseed the bare patch. Make sure you give them some extra food.

__________________
Seeing as everyone else has one - http://westwardsettler.blogspot.com/

"It is a cliché that most clichés are true, but then like most clichés, that cliché is untrue."