I live in the middle east, so the majority of my riding involves sandy trails. Riding on sand is the complete opposite to riding on mud as bigger contact area is much better for sand than a skinny one. When cars are driven on sand, tyre pressures have to be reduced to about 15psi to widen and soften their 'footprint' so that they don't dig in and sink into the sand. You don't want to dig into the sand, you want to kind of float over it. Special sand tyres for cars don't have any real tread on the either. In fact they look like big inner tubes.
The same idea of letting air out of your tyres works a little bit on bikes, but letting your tyres down to about 20psi isn't going to help your whole commute. Also, if you don't keep your power smooth and constant, and your balance perfect you're going to come to a stop pretty quickly.
I'm riding 2.2 Maxxis Ardents at the moment because their tall casing lets my run my pressures at a bit lower (about 33psi). They're a bit better than my 2.2 Mountain Kings were, but not by much.
