Ok, so not Odin, but Hadrian. "By Hadrian's Beard!" has not been uttered in major motion pictures that are insanely popular amongst teenage boys and those with the sense of humor of teenage boys (i.e., all my friends).
If you have not been listening to Mike Duncan's The History of Rome podcast, you should be filled with intellectual shame. Rest assured, I am saying bad things about you from a distance, only because Vulcan has decreed that I may not leave the foggy isle, which is currently experiencing ridiculously pleasant weather. Mike recently covered both Hadrian and regular life in the Roman Empire in the podcast, which got me thinking about Hadrian's beard.
Hadrian is widely considered one of Rome's greatest emperors and a tireless micromanager. Unlike most micromanagers, he was apparently good at what he did. Dude built a wall across Brittania in order to keep man skirts and haggis in Scotland, where they belong. He was also an unwashed, barbarian heathen.
How do we know this? Hadrian had a beard. Prior to Hadrian, civilized Romans - at least the well off ones we hear about - went clean shaven. In fact, the legends say that uberRoman Gaius Julius Caesar had his facial hair plucked by a slave in order to keep his face perfectly smooth. But, why? Especially when one considers that this shaving was not being done with modern safety razors or steel straight razors, but with iron or bronze scrapers like this:
You think razor burn is bad now. Caesarian plucking does not seem so unattractive now.
If you want an interesting answer, go check out Mark Changizi's writing on the utility of bare skin for signaling. If you want prosaic, well, then you have come to the right place. It seems to me, and this is just speculation, that the fact that shaving was a pain in the butt meant that being shaved signaled that you were a person of sufficient awesomeness to have enough time/energy/servants to engage in an unnecessary, difficult, and uncomfortable process. Judging figure skating would seem to send a similar signal.
Hadrian on the other hand was busy building island nation spanning walls and restructuring the military stance of the Roman Empire. So, he did not necessarily need smooth cheeks to announce that he was awesome.
Of course, I'm not a historian, just curious. If anyone can actually point me to some serious scholarship on the socioeconomics of beards, I would be much obliged.