Seriously, I heard that he grew it for a film set around the time of the civil war that he did between seasons, and decided to keep it. But, that's just another rumor.
And a bad rumor at that. He was in the mini-series North and South
, but that was before TNG. Late in TNG's run, another installment of the mini-series was filmed but he'd had the beard for a long time by then.
I remember the story told above. He grew it during the hiatus for no good reason and was planning to cut it off for Season 2 but GR liked it and it stayed.