I got me one of the big tire bikes, 4 or 4.5" wide. It's nearly impossible to slip on mud unless it's extreme mud, which surprised me a bit. My experience coming from cheap mountain bikes or the crossover types with much less aggressive tread. It is a heavy bike though, and I wish it had a lower gear mostly for the fun of it.
The scariest biking I did was with some friends when we were using cheap mountain bikes, starting way up a huge hill/small mountain. They were going full speed and I was struggling to keep up in high gear pedaling down hill so fast my feet are about to fly off the pedals, probably going 45mph. There was almost no shoulder on the road, cars flying by us, a 300-1000ft cliff on the other side, and those bikes don't feel too stable pedaling hard at 45mph. I'm like what's the rush wearing ourselves out racing down hill when we could have enjoyed coasting the 2 miles down?