Have you ever noticed that most pilots are clean shaven or only have a mustache? There's actually a reason why pilots don't have beards.
It all boils down to oxygen. According to Federal Aviation Regulations Part 91.211, supplemental oxygen must be provided for the flight crew if cabin pressure altitudes above 12,500 feet are reached (planes with jet engines have cruising altitudes of 39,000 feet or higher).
A partial rebreather oxygen mask
The partial rebreather is the most common mask. With this style, an external plastic bag inflates each time you exhale. The bag stores any unused oxygen so that it can be inhaled with the next breath.
It is vital that the mask seals well against the face. Unfortunately, a beard would prevent the mask from forming a proper seal and would cause a loss of oxygen to the wearer. You definitely don't want your pilot and copilot losing consciousness during your flight.
What do you think?