It depends on how deep the mud is and the type of mud etc. If you CAN get to solid ground without sinking so far in you are doomed, a skinny tire is better. But if you can't reach solid ground you want as wide as you can handle to sling more soup and stay on top.
In "no" traction situations the more mud/sand/snow you can sling the fastest while maintaining forward motion, the further you will move, unless you are digging down, then STOP!
Same thing goes for snow, if it's on the road, skinny tires are usually better in snow because they reach the road surface and don't hydroplane and float on top the snow. But once you hit the real deep stuff skinny tires get left behind.