Are fatbikes capable riding in mud? 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 ( &lt; 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)?
Depends on how viscous and deep the mud is.

If the mud is viscous like clay and maybe leaves mixed and a fat tire can float and still get traction then the bigger tire is better.  

But with normal mud and less than 6 inches deep then a thinner tire that will sink to the bottom for traction and might do better.

I was in a cyclocross race recently where we had a few inches of rain over the prior 2 days.  There were both mountain bikes with 2+" tires and cyclocross with 33-35mm.  The cyclocross were more effective.  Even muddy grass the smaller tires did better.  The bigger tires got pushed around and still did not get good surface traction. 

The other factor is the amount of mud you are going to carry.  A fat tire is going to hold a lot more mud and get heavy.