Well i found this the hard way during my first battle in the desert where i was bringing heavily armored knight and chivalric arms men.... They were exhausted before reaching the ennemy.

Finally i am bringing mainly vikings (i am the Danes), Highland clansmen, spanish janitter (yes i am controlling the Iberian provinces), some spearmen and archers. I found the spanish janiters to be better than the mounted sergent (faster, and get exhausted less).

Anyway i really hate fighting in the desert. And when you see how poor these countries are (tradeable resources and income, but Marocco is quite nice), the only reasons i would be fighting there, is if i want to get rid of the almo, or reach by land the egyptians.

In the middle east, it is much better, since you don't get all these sand dunes.