When the mud is cold if it gets up to their bellies, you've got a welfare issue. They would be much happier housed if it gets to that stage.
Until then, use straw at the entrance to the ark so they can get the mud off themselves as they go in. Then at least they should be dry and warm in bed.
You may find you need to clean out muddy, wet straw every day or two. Partly because they will be taking wet mud in with them and partly because they may start to pee in the ark as it's so unpleasant for them going outside. So keep piling the stuff you take out onto the pad at the entrance and put some fresh clean dry straw inside each day to replace what's come out.
If you don't keep on top of removing the wet straw, again it can give rise to a welfare issue, as they wouldn't have anywhere dry and warm to lie. They don't cope with that any better than we would, and can very easily succumb to pneumonia.