Part of the problem, that you have sort of identified is that the riders of one cavalry set will often not really work with the horses from another one. You might just have to accept that the horses from your main donor figures are not Hunnic ponies but work the best overall. I seem to remember reading that a large proportion of Hun armies that came West were actually formed of Germanic vassals and even Hun troops equipped similarly, so starting out with Gothic plastic cavalry might be most of the way there. Just add bowcases and a few eastern details and you're sorted...
Absolutely agree - the GB Arab sets have a few "hunnic" looking heads too, and their bodies also work - add the Gothic unarmoured & armoured cavalry, plus some "hunnic" heads, bowcases etc from the Fireforge Mongols and I think it should work well enough, especially if you are prepared to squint a little :-) The GB Arabs have separate torsos and legs too, so you can mix them up with the Fireforge ones quite well. The GB Goths are one-piece torsos and legs, but even there you can swap arms and cut spear-holding hands off at the wrist and replace them with bow-holding hands for a more 'hunnic' mix of weapons.
I did some Generic Arabs recently mixing these sets (see
https://www.madaxeman.com/main/28mm_Arab_Cavalry_1.php) and I reckon that as long as you don't have too many of the broad-beamed Fireforge Mongol horses you can get them to fit together on a base. A Hunnic army will have many Light Cavalry anyway, so depending on your basing convention you may be able to use the wider horses on LH bases too.
Heres some of the more hunnic-looking heads on Arab and Gothic horses and bodies. The two on the left are both armoured Gothic noble bodes with bow-holding arms from other sets