Does every horse pull to the right when cantering or gallop?

I noticed this on a run with a horse over some new expanded roads on my server. We were expanding the roads and changing underpasses to accommodate the horse and riders. I noticed that my Brown horse pulled to the right during a canter (gallop maybe better since there is no second speed). I had to correct to the left about every 4 seconds to stay on the road. Is this everyone's experience?

Quote from zfoxfire

The horse will turn to follow the mouse pointer. If guess if the mouse is not perfectly centered then the horse will slowly turn over time. At present it seems that the mouse lets you take a look around while the A and D have the most directional infulence (e.g. making sharp turns). Perhaps the game should eventually move the mouse pointer to align with the direction of travel if the mouse pointer is greater than 5 degrees off from the direction of travel. That way you can still take a peek left or right or behind without it affecting long-term steer

Hmmm. might check that.. ..would be nice to have a side key look similar to WWII Online while running or riding.

Quote from Wyzer

I was actually going to, and should, put that in the suggestion, to have an additional key press to allow free mouse movement, to a point, when running/riding, to see what could be coming after you. Of course this can be hazardous, as you can miss what you are running towards.

Well how am I going to shoot my bow back at you when I am galloping away if they don't implement some sort of look key?