Dwarves take great pride in their beards.
I'm sure that they trim and style their beards, but why would they ever want to shave? Even Dwarf-women take pride in their chin hair. Though, maybe the customs of the Eastern Dwarves differ.
A shaved Dwarf is a shamed Dwarf. Also, a Dwarf with a beard never needs to find a napkin.
Perhaps it is to remind them of the dwarven father's long sleep?