When I was driving in the muck, I was instructed to move at walking speed. This follows the off-roading mantra: "As slow as possible, as fast as necessary." It also reduces trail errosion.
I never had any wheel slip becasue I was driving slow and steady. I was never slinging mud. If you go fast, you're more likely to hit an obstacle, like a rock, and have the suspension compress, which brings the underside of the vehicle even closer to the rock. If you go too fast, you'll break something. If you go too slow you won't have momentum and you'll get stuck. It's about technique, not raw power and agression.
One thing our instructor said is that often people only worry about clearing an obstacle with their front wheels. They have an "out of sight, out of mind" approach and often hit the gas too hard after the front wheels are clear. This causes damage to the tail pipe, etc. The rear wheels have to clear the same spot, so go just as slow for them, too.
Here's a close-up of the mud I was driving in: