If it’s ‘sticky’ mud then it’s bad.
If your current tyres get gummed up with mud during a normal winter ride then the same will happen with fat tyres. Only worserer.
I stop riding my fatty round here (South Downs near Brighton) during the worst of the muddy season as the wheels end up weight 10kg each once you ride on anything with a clay based soil and even on the chalky bits they’re not great.
also, wider tyres tend to skate across sticky/slick mud where as narrow tyres dig in a bit more. Obviously on boggy ground this behaviour is a good thing – you float oer stuff but there’s not much like that round here.
I’d still try and get a go on one but they’re actually better as bikes for the months when the ground is wet rather than sodden, ime, at the moment we’ve not really hit ‘mud’ it’s more just wet earth and fat tyres still give an advantage.