Simple answer, for a few days no, long term, probably not either.
Dirt and mud itself really do not hurt the paint. However, if something rubs up against it, your hand, kids, whatever, dirt is like sandpaper and that can produce scratches, but they can be easily buffed out. The mud staying there holds in moisture, which again is not a problem in of itself, but if there are any compromises in the finish, the mud can hold in moisture and accelerate rust, but only if there was already a problem. In this weather, leaving it on is less of a problem than in the summer when the sun will bake it on and it is harder to remove. If you are having all the rain we are having, that will make it easier to remove.
Particulary since you have waxed it, you have nothing to worry about.
After six years, 106k and tons of mud on my truck, I have no body rust at all. I do keep up with any scratches and wax it a few times a year.
Also, every time I get it muddy, I leave it on for a few days, just to show off.