I'm not just saying this because Paul Anderson is way hotter with a beard

Looking at tigers I'm feeling that it should definitely be canonical that Moran has a beard not just a moustache. They have that big ruff of fur as well as all the whiskers; when Moran is linked so closely to the tiger give that man more facial hair. (Paul Anderson is definitely way hotter with a beard though)

I also think there are various reasons why Moriarty having a beard (though a bit less neat than Moran's) does make so much sense but on the other hand him being specified as clean-shaven in The Final Problem when in the Victorian era being clean-shaven was associated with homosexuality is extremely interesting.