I've basically always seen them with either beards or mustaches and lots of whiskers. Was this due to their typically older than average age, or was it more of a mandated style among them?
It is more of a myth than a fact. A member of the Old Guard Grenadiers or Chasseurs could be as young as 25 or as old as 40. The Old Guard was also used as a depot for providing NCOs and officers to the Young Guard and the Line, so most of those who were older and more experienced, and literate, wouldn't stay in the Old Guard but would be senior NCOs or officers elsewhere. Let's look at an example. An illiterate 18 year old in 1792 at the start of the war would be 28 in 1802, and 38 in 1812, 41 in 1815, so not that old. There wouldn't have been that many who would have survived that long to still be on active service and not invalided! Although there were stringent requirements for entry into the Old Guard, these were relaxed and suspended on an ad hoc basis, especially post 1812 when the Old Guard were increasingly used as cadres for the expanding Young Guard formations. Lachouque's "Anatomy of Glory" is good, if a trifle uncritical.....
In the Napoleonic French army (as well as others of the period) the average soldier was expected to be clean-shaven, with moustaches being expressly reserved as a distinction of elite units. René Chartrand writes of Napoleon's army: "moustaches were the prerogative of grenadiers and hussars" (as well as voltigeurs, which whom he forgets to mention for some reason). As well as being allowed to wear moustaches, the Old Guard, as an additional privilege, "were allowed to keep their queues and powder" (Chartrand again)- that is, to dress their hair in the style of the Ancien Régime.
Anyway the above was the general rule: as exceptions I would note that the sapeurs of regular infantry units customarily wore moustaches and full beards (as can still be seen today in the Foreign Legion), and some regular NCOs wore moustaches. The mounted units of the Old Guard went clean-shaven, including the mounted grenadiers but excluding the Chasseurs and Mamelukes. André Joineau, in his very comprehensive study of the uniforms of the Old Guard, depicts all foot officers as being clean-shaven except two subalterns, both of whom wear moustaches.
R. Chartrand, "Napoleonic Wars: Napoleon's Army" (1996) (Brassey's)