Great! Thank you all. I always wondered. Although I spent a lot of time there, both daytime and nighttime, I never saw a strange creature. I'm not too much of a believer in them anyway. Maybe the goat-man knew that?

TXGenWeb had this to say:
MOSQUE POINT PARK: The shelter was constructed by the C. C. C. in 1934 on the site of an Arabian style Mosque erected for the Moslah Temple in 1918. The Mosque burnt in 1927, but the point's name had been changed from Reynold's Point to Mosque Point by then.

There is some discussion about the Masons, Mosque Point, and a whole lot of weird stuff, which I totally did not understand here:
http://www.imsfsc.co...html?1073263706

I looked around for a picture, to no avail. My memory must have faded over the last 20 years. I thought there were 2 fireplaces. Thanks for clearing that one up.

Back in the '80's I served at CAFB. Being from Tyler, it was a nice assignment. I lived in Ridglea (?) off of Vickery, and used to walk to the used record store by Monnigs a lot. I think my favorite resturant was Caros out on University.
A civilian friend and I used to go to this place by Lover's Lookout on Lake Worth. It seemed to be what was left of a house. There were rock walls on the outside perimeter only, and they were only 3 feet or so tall. There was some type of cement for the flooring and two fireplaces with standing chimneys on the inside. On the lake side, there was a trail which led to an uncemented stone staircase. I can't remember how many steps there were, but there were quite a few. As I remember, the steps led down to a HUGE rock partially inside the lake. The rock made a natural dock, of sorts. It was a perfect swimming spot, of course - I didn't know there were 'gators in there at the time!
Does anybody know what purpose the building served? I have always wondered.