I am from Washington. I know your helpless feeling. It pours and pours and our paddock gets -very- nasty, to the point that I've lost shoes out there and not found them until summer. O.O The best thing to do is to get ride of the mud. Do your best to push it out of the way, build banks to act like a funnel to a safer place. And then add gravel.
If you are not in an area like mine, where it's not as bad :) (then I would consider you lucky!) Just add gravel everywhere! Your horse will not slide on the mud anymore. It will be deep until she packs it all down. Don't be conservative. Get a good amount of gravel in there. Good stuff. :) Horses usually will avoid the slippery mud when they can, so even if you can just make a path using the gravel, she'll be better off. Hope that helps! :)
That is how it was at my place for a good long time this spring. More rain than I knew what to do with.
I ended up confining my horses to a smaller area (that they destroyed) with dry shelter available to them. I went through a boat load of hay keeping them busy (bored horses get in trouble, too much trouble).
Thank goodness it isn't like this too often, it would be terrible. Do you get a lot of rain?
To say we get a lot is being modest. It's raining 8 months out of the year, on a good year! However, the mud is because we have -lots- of clay in our area, so the water has no where to go. So yes.... we get lots of rain, and lots and lots of mud! :)