LAist had an article on this, but I like this one better.

Tropical Ice Gardens opens in 1938 at the SW corner of Gayley and Weyburn. Hard to judge the exact extent, but it looks like it runs along the whole length of Gayley from, say, Coffee Bean&Tea Leaf to Cafe Elysee. And then to the west quite a distance. Open-air, year-round skating rink in Westwood. Crazy!