You have my best wishes...
I raise cattle and have done some studies of grass.
You will note that there is very little grass in the photo and sparsely scattered low woody plants.
There is a reason...there is insufficient rain to support real grass and the woody plant roots suck water for an area around each plant, preventing any other plant growth.
The amount of grass a cow and calf eat in one year is called an animal unit. Four sheep or goats and their annual lamb/kid equal one animal unit.
My judgment from afar is that country requires about 100 to 500 acres to support one animal unit. You can do the math as to how many cows + sheep you can run on 20 acres of that country.
Thus, you will not be doing supplemental feeding, but 100% of the animal feed you will be bringing in, regularly, and providing to the animals. Thus, you will need to provide a shed for storing, in bulk (feed in sacks is EXTREMELY expensive) all the feed.
Essentially, you will be running a feed lot to fatten animals for slaughter. If you are considering a breeding operation, a bull equals 1.5 animal units and a ram is about two ewes. Consider that the kind of pens you need for cattle are different from sheep. And, you can manhandle a sheep into a trailer, not so much for a cow.
Do you have a known, reliable water source capable of supplying all your needs...do you have access to irrigation water??
In Texas, sheep and goat operations either are nightly put in a shed or have a guard dog or donkey to ward off the coyotes, or are out of business. I'm sure you have coyotes there, so you need to protect from them, 24/7.
Is there any shade on the place?? Animals will need this to avoid heat stroke in extremely hot weather but I don't know how hot it gets there.
All things considered, I cannot overemphasize the benefit you will have from consulting with a local expert. Personally, I think you should contact these folks who are extremely familiar with the water requirements for the various grasses which are native in the area.
http://www.colostate.edu/Depts/SLVRC/CROPWATER/srmac10/cabotSRMAC10.pdf
The above people, without question, will be able to answer your specific question related to grass.