If I've just shot an arrow at an enemy and while the arrow is in the air I load a new arrow, but then the enemy dies from the first arrow and I'm stuck with an arrow in the bow. Instead of just planting it in a tree and grab it again, is it possible to unload the arrow from the bow?

The simplest means is, as you have discovered, just shoot the arrow into the ground and grab it. There is another means, that is more tedious, but at least it can save you any applied poison and not waste a charge if your bow is enchanted:

Once you get the acrobatics skill to 50, you gain the 'dodge' perk. If you have an arrow nocked, start to move in any direction and execute the dodge manuever, you will unnock the arrow.
More info on the dodge manuever here: http://www.uesp.net/wiki/Oblivion:Acrobatics

If on PC, there are mods that can allow one to denock arrows without doing the dodge manuever. I'm on PC, but have been using the dodge to denock manuever so long, it is second nature now.

I always face the bow into the ground and shoot it. Catching the arrow when it comes back up feels so cool. B)

Unfortunately you lose the poison, so the Acrobatic perk seems the way to go.

This is one of the things that make you go "huh? what the devs were thinking?"