Something most folks seem to kind of forget is that around the early Crusading period quite a few of the better-equipped Middle Eastern warriors actually wore more armour than the Catholic newcomers (the prevalence of powerful composite bows and increasing numbers of annoyingly limb-severing sabres in the area may have had something to do with that). And it didn't get all that lighter later either. Cavalrymen might wear several mail hauberks and a lamellar corselet atop that for good measure...
One also needs to keep in mind the East Romans/Byzantines and first assorted locals (like the Palmyrans) and Persians (ie. Parthians and Sassanids) and later Muslim Arabs and Turks once they got access to enough manufacturing base kept gleefully throwing massively armoured cavalry at each other in the region for a long time, and kept doing so after the Crusaders had been served the eviction note. Mind you, the Mongols joined the fun for a while too. Armoured horses weren't exactly rare either, and I understand one of the biggest problems with barding even in milder climes tended to be heat exhaustion; yet the beasts down there appear to have markedly failed to keel over en masse due to heat strokes.
That doesn't of course mean less armour wouldn't be rather more comfortable, but one suspects popular commonplace rather overrates the heat issue (besides being rather ignorant of the actual military powers involved). I'm under the impression even very heavy troops were normally right fine so long as they covered most of the metal from direct sun (the local "Franks" adopted local styles of dress rather quickly no doubt partly for this end) and were supplied with enough water.
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