Well, not sure about crosshair (not like you need it, its centered in 1st person, you can make a "mechanical" one), but I'm fairly sure you won't be able to get out of first person.
A handicap for horse ranged? Yes. It's not much of a problem firing in the front, but shooting to the side and especially to the back will be risky since you don't know where you are going, and have little awareness then. I remember doing it on purpose (riding around in 1st person view) with a crossbow riding through the village map, the feeling of speed is awesome, but of course, your situational awareness suffers.