Hi Marlene, don't worry - that seems to be a normal first response of some big horses when getting to know a pony. You can check out the beginnings of Pia's diary. I thought Titum would kill her, and with Bacardy it was the same (only that then I knew better).
For us the solution was to build pony fences and teach the ponies how to use them before putting them together with the big horses. That is, we buildt fences that were high enough for a pony to dive through under them but too low for a big horse. The problem is just when the big horse chases the pony in the wrong place, one where there is no pony fence. So with Baca I did it a bit differently: I put Titum in the middle of the pasture and surrounded HIM by a pony fence. In that way, no matter where he chased Baca, Baca could always get away.
Worked like a charm, and after a few weeks Titum got tired of even trying to chase Baca. Now we don't need the fences anymore at all - they have become a happy herd.