Firstly, to Renojustin:
Well, MtG's ideas are strange to say the least. However, there were at least 2 fantasy strategy games with strong Nomad faction of Arabo-Persian kind. I mean Master of Magic (of course!) & Age of Wonder. As for melee unit - ghazi will probably be fine name for these!
-- Historical near-OT warning --
Actually, Arabs of early era often used melee infantry (which we can know from Byzantium military textbooks), fighting in falanx-like formation. Their military is also often depicted riding 2 on 1 horse (which was actually a way to transport foot archers, & can be translated to Dom3 engine by having said archers with map move 3). What they didn't had are composite bows, at least of Mongolian or Turkish quality, so their early cavalry should probably have just shortbows. Also, Arabian cavalry preferred melee (charge) attacks, which led to their defeat by Frankish heavy cavalry of Carl Martell.
The main "fantasy races" in folklore of the region were often named as "daw, jihn, ghul, and peri", in that order, at least in Persian sources (I have no English version, so probably spelling may differ). Daw were servitor race, relatively stupid, but strong and able to shapechange. Jihn we know. Ghul were maneaters with some magic skills, but often depicted as having no armsor legs. Peri were a race similar to Dominions Vans/Thuatha, but, according to Persians "made by Creator not from clay, but from fire", their women were said to be most beautiful & they lived in their own cities.
At the time of Crusades we see appearance of Hashishiin mentioned above. Also, at that time Arabians began use of Turkish mercenaries & slave warriors, which introduced their composite bows (though these also were not "light cavalry", being armored in chain mail!). As war against non-beleivers became less popular among civilised citizens, the special ghazi were introduced - they lived in their training camps at the borders and helped to defend these against Frankish barbarians (i.e., Crusaders
).
Later still, Turks mentioned above became rulers in the region. The best known is, of course, Osman Empire with its Janissaries and Sipahi. (Mongol influence I never heard of, unless you count that Tamerlan actually saved Constantinopolis by crushing Bayazid the Lighning's army at Ancara...
)
---end of near-OT---
According to this I would make first era based on lightly-armored troops, supported by recruitable members of genie races. The medium period will include medium-armored horse archers, sacred ghazi & probably some armored infantry, though the latter was not numerous. Plus sacred Assassins, of course! The late period should include mail-armored cavalry and Janissaries of Osmans. Of course, heat preferrence, as was already mentioned. Camel caravans I would make recruitable animals with negligable combat ability but providing supplies. As for eunuch assasins - unfortunately, Dominions engine doesn't allow poisoned coffee as weapon...
I would also move this discussion into Mods area unless official version is going to be produced soon...