I'm sure it's been said or alluded to - but it's basically an unwritten rule based on a few letters about not having beards and a few references in the magazines that associate beards to negative things.
The reality of it is that it falls right in line with one of their favorite quotes - "those faithful in what is least will be faithful in what is most." They usually use this as an exhortation to be faithful in small things because you'll be strengthened, but there's actually a clear psychological effect that causes people who are willing to submit to a small display of obedience becoming more likely to obey more significant orders afterwards. It's a similar effect as the source of people "throwing good money after bad" at a poker table, or in business. They've made a small investment and rather than come to terms with the fact that this was a wasted investment, they'd rather make ever increasing investments.
I had a discussion with a friend of mine the other day and I got to talking about all the unscriptural rules that the GB puts upon JWs, likening them to the pharisees that jesus said had invalidated the word of god through their traditions of men. He maintained that they were there for the protection of the stupid/weak ones - i.e. no beards because it might stumble someone. When I told him that their order not to have beards stumbled me, he just stared at me and changed the subject.