Eh, no the bows wouldn't be outranged just because they're shorter. They seem like composite bows, which were superior to longbows and crossbows (if you make em properly).
Horn and sinew compress better than wood, and that is almost certaintly what they made them off (since their desert would be as devoid of wood as the steppe warrior's who perfected the composite bow.)

But I think that the Borderlanders would be able to beat them, evauntaully. You have your horse archers incircle them, firing. They would take casualties, but then you charge with your heavy horse. Once the Aiel move foward to take those heavy horse, you take them from behind with fresh heavy horse.
I believe that is what the essential tactic was in New Spring, at the begging with Lan.

If you were Mat, and you could try and have pikes incircle your bows and crossbows, and have them duke it out, but they would take heavy casaulties from trading arrow fire, and the Aiel might not be stupid enough to charge, or be held while flanked. (Also I think a tactic used against the Shaido, if memory serves).