What is the basis of the LDS/Mormon prohibition of facial hair for men?

I have read in a few places the LDS Church has at least a general practice, if not an official teaching, that prohibits men from growing facial hair--at least for men in any position of leadership. Apparently, Joseph Smith was "clean shaving", but many of the other prophets and leaders in times past did have significant beards and moustaches. So, my question concerns what the basis is for this teaching and when that basis came about. Is it an official church teaching or an unwritten policy, and is there any reason given for why facial hair, which God seems to have intended for men in some way, is inappropriate or wrong?