Hi Bill and welcome! I had my girls on a wood floor for a long time before I moved and got a barn with a dirt floor.. so much nicer.. but if you can't, you can't..
what I did was put a heavy layer of Sweet PDZ (found at most horse supply places) which changes the chemical composition of urine so that it doesn't produce amnonia, then a heavy layer of shavings.. if you don't have a lot of goats - yea, you don't have any now, but they are like potatoe chips, you can't have just one! - then you can clean up wet spots and berry piles pretty easily, and sprinkle more Sweet PDZ on the spot.. I only did it in the mornings on nice days and of course more often on nasty days...
On those rainy days, they will stay in the barn on their own and probably won't venture out into the mud untill it starts to dry some. As long as they have a dry place to go their feet should be fine.. it's only when they can't get 'em dry that you run into problems..
My barn was initially built where water runoff from the pasture hit the west side of the barn.. corrugated roofing material was placed up against the barn and angled away, sort of like an L , the trim came down over the top of the L and dirt was piled up against the lower part to keep water out.. I've since added a bit of dirt to the inside, and the girls have a little 'step-up' to get into the barn, and the floor stay's dry, even in wet wether..
Oh yea, good choice in goats...