His hair colour isn’t mentioned in canon except that his moustache is described as “grizzled”, so probably at the point he appears his hair generally is grey or going grey (which also fits with Watson describing him as old/elderly even though he’s only in his fifties). What colour it was originally though is anyone’s guess.
SH: Little Moran by NightMagican
Title: A Most Intimate Experiment
Characters/Pairing: Sebastian Moran/James Moriarty
Warnings/Contents: explicit sexual content, D/s
Summary: Professor Moriarty proposes an experiment