Henricus has a nice trimmed beard, it may be to compensate for his early receding hairline, or to have a way to determine the shape of his chin, but he has a beard. Aran and Teleri (the latter naturally, being a woman and all) did not have beards.
Funny noone has spoken about the longbeard on his magus to accompany the pointed hat...
Various cultures have used pointy hats, for various reasons.
en.wikipedia.org/wiki/Pointy_hat
Associations with wizards can be inferred where one will.
Enchanted headgear could make interesting accoutrements, as could enchanted combs, hair nets, hair or beard rings, and the like.
Inventing a Formulaic spell to perfectly shave/trim and/or coiff one's hair would require only a minor amount of work in a season of study. It's something that a moderately experienced Magus could do while completing another project, and once the spell was recorded it would represent only a small investment of time to learn. Or, to put it another way, for maybe 5-10 Levels (for more elaborate versions), a Magus could readily have it as part of his starting grimoire.
I would say that it would depend on the house and the Magus, especially their country of origin.
I wold think Tremere being modeled on the roman legion would be beardless. Wilderist Bjornear are less likely to shave then harmonists. Jerbiton would probably follow the most cutting aethetic tastes.
Being male and Not sporting a beard could also be part of the general 'creepieness' of the gift.
Santiago is VERY proud of his Hulk Hogan style 'tache and strokes it when he is deeply in thought...
Given that my current magus is a maga... 
Over the years I have had a wide variety of hairstyles for my various magi; bearded, non-bearded, bald, long hair, short hair, mustachioed. All of this depends on the particular magus (or maga).
Dwarves love bearded magas!
Oh man. Tears in my eyes. 
Obviously Julia is gonna have to work on a new spell...
According to my naming dictionary, the name "Julia" actually means "bearded"...! 
YEARGHHHH!!!!
THE HORROR! THE HORROR!!!
Xavi
I think that would qualify as a significant physical effect caused by Strong Dwarf Blood. Though so would having deformed feat (a common trait amongst the Dverge).
Magical hairstyling (and beardstyling) is probably very popular in the Order. A little Creo for touch-ups, some Muto and Rego for colouring and styling, and almost any coiffure imaginable could be achieved.
So would being a magical hairstylest count as an affront to the dignity of a Magus? Again, remember the Spartans--it has a long and distinguished history.
The spartans used magic to style hair? Who knew? 
Well, the Spartans knew this, to begin with. Apparently, this was as important to them as body building, fighting skills and the rubbing of oil on ones body.
AFAIK The Romans did much prefer the shaved faces, but the quality of metals was less than perfect. So razors were poor at holding a sharp edge, so shaving was often unpleasant. But the price we pay for looking good...
Is there a book on the spells the Spartans used? 
I think you missed my joke, which was about Arawn's post implying the Spartans were an example of a long and distinguished tradition of magical hairstyling.
See how history embellishes things out of all proportion?
The truth is that Joe Spartan happened to casually mention that Percy Spartan's new coif was enchanting and suddenly everyone was screaming wizardry!
Heaven only knows what we'd be saying today if he'd said it was [b]divine[/b]. 
Hence the widespread use of depilation. Each and every hair plucked out rather than shaved. It lasted longer, and didn't require the same maintenance in the field.
Romans were masters of iron and bronze, however. The former they acquired from the Etruscans, who were legendary for their iron-working (actually, they acquired a lot of techniques from many different people).