...then again, those animals are big enough to wade many rivers anyway...

Personally, back when I was making my BI-feature minimod for 0.8x I followed the rule of thumb that all infantry without actual body armour (starting at leather/linothorax level) or greaves, and not burdened by an overly large shield (bigger than what eg. the Peltastai have, ie. about 2 points in EDU terms = Right Out) or weapon (eg. long spears or two-handers) could swim. Ditto for any unbarded horse whose rider's war gear didn't exceed the breastplate-greaves-shield/lance level - horses are AFAIK strong enough swimmers, and that amount of war gear shouldn't burden a mount that qualifies for such heavy-cavalry duty in the first place overmuch.