We've had a similar problem at the pool. Except with us the pool was leaking. One of the guys built a HUGH drain to dry out some of the land. For years the old guard said "it's an underground spring, it's groundwater."
Until the year of the drought, when I finally got fed up and screamed "There IS no GROUNDWATER!"
Anywhere horses travel back and forth in winter can turn to mud, the lucky part with us is that the soil really is pretty sandy and it dries out pretty quick when the rain stops. I didn't have bad mud in previous years - not till we filled by the gate and trapped and held all the water that comes from the driveway. That, in hindsight, was a big mistake.
But I always had that lake in winter.... and always thought it wouldn't be too hard to drain it, if only I had a man with a shovel ;~D