Well, here's the thing. I'm pretty sure shooting a bow and arrow accurately on a running horse is quite difficult in real life. I plan on shooting the bow and arrow most often from my horse standing still.
I've got the beta currently, and most of my experience has been with mounted archery. It
is hard to aim, though I think I'm getting better at it.
I've never shot a bow from horseback, but my real life experience with shooting a bow on foot leads me to suspect that, yes, it would be very difficult. And in game, I do take plenty of shots while the horse is standing still, because it's easier.
Shooting things like wolves and fast melee bandits is pretty difficult, unless you can kill them before they get close to you. Once they're on your horse's tail, it's very hard to get rid of them.
Giants and mammoths are my favorite targets from horseback

. I never really went giant-hunting before this, but I've cleared out around 3 giant camps since the beta with my horse archer. Sneak archery is still the faster, more efficient way to kill them (and to kill anything, really), but horseback archery lets you keep your distance and avoid their nasty clubs. And they make nice big targets, too.
The controls are rather weird, though. You need to use both the mouse and keyboard to change direction... but once you are looking at yourself directly from the side (9 o'clock or 3 o'clock), the arrow key will only turn you in one direction, not both. If the horse is aimed roughly between 12 and 3 o'clock, or 12 and 9, at a 45 degree angle, the arrow keys will move you in either direction. It doesn't feel very intuitive, and the weirdness of the controls is probably the main reason that every now and then, in the heat of battle, it feels like the keys are turning me the opposite of the way I want to go.