With only one acre for two horses there is really not a lot you can do. Here are some suggestions and after raising horses for about 40 years I have tried just about everything but who knows? Someone else might come up with something new.
Split your acre into thirds. Confine the horses to one third at a time.
Con: This is really too small an area for two horses and they cannot run and play, possible fighting. The area they are in will immediately be reduced to bare dirt.
Pro: The other areas get a bit of a rest. Find out what type of fast growing annual grasses work for your area and plant them. In my area of the south brown top and silver top millet are fast growing for the summer and give the horses fresh greens. Tons of people say you shouldn’t graze horses on it – mine did just fine.
Confine your horses to stalls during the night and only allow them out during the day to graze for short periods.
Con: I hate confining horses to stalls – I don’t think it is healthy, mentally or physically, but lots of people do it.
Pro: It is the only way that small of an area is going to be able to grow anything.
If you are feeding hay outside put it in racks up off the ground - such as
fence mounted racks. Hay on the ground, especially round bales, suppresses growth beneath it - great if you are growing veggies but not so much if you are trying to grow grass.
I am assuming that you have no other options and one acre is what you are limited to.