Fatbikes are traditionally used for sand and snow which are surfaces which are loose and liable to break away under the weight of the bike and rider. They are also materials that don't generally stick to the tyre.
A muddy surface such as a peaty or poor-condition dirt track after rainstorms would also provide some likelihood that the material will break away under the tread. However, mud is often sticky and likely to stick to a tyre.
Therefore is mud more or less likely to stick to a fatbike wide with and diameter tyre than a small skinny ( < 2.5 inch ) mountain bike tyre where more pressure is being exerted over a small surface area, or more extreme a cyclocross tyre (these guys seem to ride and corner in muddy conditions successfully)?