You're far more likely to tear up the soil and perhaps even worse (e.g. create ruts that lead to further drainage and erosion problems) when you bike through mud. It's one thing to ride on a trail that has a few soft, muddy spots, but the Leave No Trace principles intended in part to preserve soils and prevent erosion mean not going out of your way to ride on a trail that's very muddy and therefore prone to damage. Some places are just too fragile for biking (or hiking). You won't be allowed to take even your sweet fat Pugsley on a sand dune preserve, nor off the marked trails in a fragile desert park; for the same reason, you shouldn't take it on trails muddy enough that it leaves tracks, IMO.

BTW, I'm envious of your new ride, too. Good thing we get little enough snow around here that I can tell myself it would be a hassle finding great places to ride it. :-)