Just try it.
We did. Padding, yes. AND light cloth covering to disperse direct sunrays, too. Did you know that Middle Asia nomadic people actually wear such padded clothes to protect themselves from heat?
Arabs, yes, rarely weared armor. And iirc, never leather one...
And, for glory of Lord, what regular armies do you mean in medieval setting??
Byzantines probably?
The legends argument, though, is valid.
So do you mean that MA is then Mohammed's / 4 Pious Khalifs' time? I would prefer it to be somewhat later... Though we probably can mix & match them into something interesting...