kerach and kereach

It was frosty here this weekend, so I got to thinking - is there any connection between the homographs קרח kerach - "ice" and kereach - "bald"?

Even Shoshan discusses the verb root קרח (as found in Vayikra 21:5), and says that the meaning is "to pull out hair", and notes that in Arabic the cognate is qara'a - or קרע in Hebrew. In Hebrew this root means "to tear, rend." (Meshullam Klarberg writes here that only in modern Hebrew does kore'a mean to tear by hand, while in Biblical and Talmudic Hebrew it could also mean cutting with an implement.)

As far as kerach ("ice"), a footnote in the Ben Yehuda dictionary points out that the Syriac cognate primarily means "storm", and speculates that this might be a connection between the two meanings: a storm can tear the leaves off of trees (making them bald), and a storm can bring with it cold and snow.

Another theory is proposed by Gesenius, that the common root means "to make smooth", which applies both to ice and to a bald head. That might be a simpler suggestion, but his book was written in 1836, with far less exposure to research into related Semitic languages. So perhaps the evidence here leads to a more complicated conclusion.

What about the name Korach קורח, found first among the sons and leaders of Esav (Bereshit 36:5, 36:16) and most famously the Levite who led the rebellion against Moshe. Daat Mikra (Bereshit 36:5) says that it probably means a bald man (which stands in contrast to the "hairy" name of Seir - also found in Esav's family).

This made me think: while certainly a bald man might get a nickname referring to his baldness, why would anyone name a baby that? Then of course, I remembered that my kids all entered life rather bald...