Are fatbikes capable riding in mud?
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.