As Alesplin puts it, it is common practice to stay off of trails that are muddy.
I'd like to expand on his answer a little. I think there are a few factors that come into play with a question like this.
One of the biggest contributors of damage to a muddy trail is large amounts of traffic. The more people that use the trail, the more damage will be done. If you are one of a few people to use a trail, you most likely won't do any permanent damage. The worst thing you will do is create ruts, that when dry are not the nicest things to ride on/in.
Ruts can also lead to other forms of damage. A rut will collect water, which will not run off the trail. Quite often, these puddles of water will get bigger and bigger until they consume the width of the trail. This, I think, is when the real damage occurs. Trail users (both rides and hikers) will most often avoid going through the standing water and simply go around (at the cost of the surrounding vegetation). This can lead to parts of the trail being expanded unnecessarily, and there will still be the problem of the expanding rutted water hole in the middle of the trail.
In the end, if the trail is used very lightly, riding in the mud will not do much damage at all. For most trails though, it is best to avoid the muddy ones. Of course, there are always sections of trail that are muddy, no matter what. Those are a whole other matter of how to properly build and route a trail. Get dirty and have fun.