I'd say you're spot on about the mud, because it looks waterlogged. Give it some time, let it dry out first.
Milk is used to help generate better pasture, I think the rate of application is around 10% but it's been a while since I've read on it. Used as foliar is 10% mix, good for some species of PM. It will introduce good things like calcium, but you can use too much so go easy. Probably better as an occasional thing, as I recall the pasture applications being something like 2x/year.