A thing to be aware of if you put straw down on mud:
it will improve things for a while, but eventually the straw will decompose and create *worse mud* -- deeper, suckier, slower-drying.
So if you're just using straw as an emergency fix that's fine, but you really really wanna remember to rake it out in late spring or summer, once things dry up some, and fix the mud problem PROPERLY (i.e. durably). A durable fix means diverting as much water as possible, by means of eavestroughs and ditches and so on, and then if still necessary, raising the ground up higher, ideally using hard-tamped gravel (over which you replace dirt, sand, or whatever you prefer).
If you're not going to do that, at least take out the old straw and come next wet season put in *fresh* stuff, or woodchips, or something like that.
Pat