The best advice I can give is to choose very carefully where the new goat shelter & pen will be to avoid water issues. Don't set it at the toe of slope where water will be running on to the area, and don't set it in a low spot.
It would be best to strip the topsoil from the area and bring in a gravel product to provide dry footing and good drainage.
Adding gutters to move roof runoff away from their pen is very helpful as well.
I'm not familiar with the mulching method but I don't like to add any organics to animal pens. The use of hay, straw, wood chips, etc. all just eventually contributes to a mud issue even if it helps initially.
It would be best to strip the topsoil from the area and bring in a gravel product to provide dry footing and good drainage.
Adding gutters to move roof runoff away from their pen is very helpful as well.
I'm not familiar with the mulching method but I don't like to add any organics to animal pens. The use of hay, straw, wood chips, etc. all just eventually contributes to a mud issue even if it helps initially.