I find a heavily armored horsemen too much of a burden in the desert but if you happen to have them there then unmount them if you can. The advantage of having a horse is being able to run them around and the heavy armor cuts this really short. However, heavily armored troops are still effective if you can get the enemy to engage in melee.

I had at first followed the game guide's suggestion and sent my old Urban Militiamen into the desert who did quite well. Later, I sent in some extra CMAA who shredded to pieces anyone within sword reach... I did of course make sure not to chase anyone with them though. I found all in all that desert combat was not that difficult because outside of the exhaustion you mostly faced lightly armored horses and infantry.