Individual topic
Issue: Is Wider Better?
Off-road traction is all about maximizing your tires' contact pressure, which is largely a function of tread void ratio, or the ratio of rubber tread blocks to the open space between them. A high void ratio will put more of the vehicle weight on a smaller amount of rubber, increasing the contact pressure. A larger tire with the same tread will decrease contact pressure, although the void ratio remains the same. Similarly, a lighter vehicle will have less contact pressure than a heavier one using the same tire.
Here are some general rules to keep in mind.
For sand, size is everything. The wider (not necessarily taller) the tire, the better the flotation, and the idea in sand is to stay on top. Little or no tread works fine in sand, and the rounder the tires shoulders, the better. Also, the less void and the more rubber, the better. Vehicles with a lot of power can run tires with seriously aggressive tread.
For mud, tire bite and power availability should be matched. Light vehicles can benefit from wide tires, allowing them to float over the worst, while heavy rigs may be better off with skinnies that can find traction beneath the muck. Either way, the taller the tire (if there's power to turn it) and the more void, the better, because height keeps the drivetrain from hanging up in the goo.