You are absolutely correct. I visited Jerusalem last October. When we went out, the first evening there, It was the same temp/humidity I am used to in San Antonio.
It does snow more often in Jerusalem and Bethlehem than it does in San Antoinio. But just a little more up into the Texas Hill Country would be a pretty good approximation. San Antonio is at 29:46 N latitude, while Jerusalem is at 31.47 N. Jerusalem is also higher at 300 meters ASL than San Antonio, which is only around 700 feet, so the difference in elevation in not so great. And two degrees of latitude is only about 120 nautical miles so Somewhere around Ft. Hood would be very similar, if drier because of being farther from the water, and because of other geographic factors.