On the 5th mission (tip of the spear) in halo: reach at the beginning, Kat is driving the warthog she and noble six are in. If you notice she has her left hand on the wheel, and the right one on the gear shift. As she nears the bridge she can be seen shifting. So warthogs are most likely manual.
bungie probably left that out of normal gamepla because players would get sick of it really fast.
On the Halo Nation page for the warthog it says that it would be impractical to have a manual transmission because of many reasons. This was probably overlooked by Bungie.