This is one of the best questions I've seen for ages. I've looked for a while, but can't find a definitive answer, but hopefully I can give some useful information.
Two things: the up bow mark doesn't really describe an upward direction, but instead that the bow is pushed, rather than pulled as in a down bow. So, this helps to explain why this doesn't use an upward pointing arrow. The orchestration book on my desk, Walter Piston's Orchestration, points out that these signs are,
more clearly expressed by the French tire (drawn) for down-bow, and pousse (pushed) for up-bow.
I figured that trying to find out when bowing marks were first used might yield the reasoning behind the symbols used. This webpage has some detailed information about the early uses of bow markings in string music. Interestingly, it mentions that the violinist Ferdinand Franzl used bowing marks, but that they were,
inverted versions of the modern signs
At the bottom of the webpage there is a link to another webpage describing the continuing development of string bowing markings - but unfortunately the webpage linked to no longer exists, oh well!
Just one observation of my own, the upbow on string instruments is more suited to creating a crescendo (getting louder), with the downbow more easily producing the opposite; to my eyes this makes the upbow symbol "look right" (it is similar to an upward crescendo symbol). Equally, the downbow on strings is more effective at creating a strongly accented "heavy" articulation, and the downbow symbol somewhat resembles the marking for marcato.
Sorry, to not be able to give you a definitive answer - I hope this post gives you some useful information though.
EDIT: @tohuwawohu points out here that the upbow marking resembles the tip of the bow (where you start when executing an up bow), this "pointy" marking also being appropriate as the tip is also called the point of the bow (punta d'arco in Italian, pointe in French). And, the downbow marking resembles the frog (or heel) of the bow, where you start when executing a downbow.
As I say, @tohuwawohu deserves credit for this additional information.
UPDATE: the search continues, especially considering @11684's comment above (below the OP's question) - I'm trying my hardest to find a source to back that comment up.
In the meantime, I have found an example which uses t (tirer, to pull) for down-bow and p (pousser, to push) for up-bow, as mentioned above. It can be found in this book. See extract below from Principes de violon (1718) by French violinist and dancing master Pierre Dupont: