Both horses and chickens can be pretty aggressive to plants if they're in a small enough paddock, so you might consider making very small paddocks and letting the horses eat and trample the heck out of the pampas, then move them to the next paddock, and put the chickens in the paddock to condition the soil, then replant with native grasses and forbs. You might have to dig out some of the pampas "stumps" by hand.
It's possible you might need to feed some hay to keep the horses in the paddock long enough to really suppress the pampas. You probably don't want to have to do this, which is why I thought goats might be helpful, because they're more likely to eat something not very palatable like pampas. But then you'd have the trouble and expense of keeping goats.
It's easy for me to theorize like this; though I have a pasture that needs restoration, I haven't done it because of the trouble of installing all that fencing.

(I have sheep.) Horses can be contained within a perimeter fence with just an electric tape, but goats and chickens will need electric mesh.