In our case the mud was because the largest patch we grew on was mostly bare due to how poorly our grass had handled the previous summer and how trafficked it was. I haven't noticed any issues since the clover grew in, except for areas where it was still immature or had been killed before reaching maturity by the kids and dogs, which I just reseeded a week or so ago.

I have noticed that we have multiple layers based on the different varieties though, with some growing taller and some growing closer to the ground. None of them are flowering yet so I couldn't say which they are with certainty. I'm mostly going off the different patterning and leaf shapes. Its possible that contributes to producing less mud, I'm not really sure.