A warhorse has been trained for war and wearing armor. The MM specifically calls out the warhorse as the one animal that can wear armor by default.
The DM can, of course, allow the ape to be trained to wear armor (and potentially, even use weapons) but that can't be assumed. The DM is also well within his or her rights to say, no you can't have a war-ape.
A wizard probably has a 16 to 20 Int but he still can't wear armor (by default).