I've been researching the Houston Live Stock Show & Rodeo. I had no idea the Dew family of DeWalt was so instrumental in managing the show back in the 1930s. They organized rodeos on their various ranches (including DeWalt) before the Houston Fat Stock Show began in 1932.
By the way, that was its original name. Here's a lengthy article about the history of the event. It explains the name change as the rodeo became more prominent & 'fat stock' no longer projected the right image. It's lengthy, but you may want to look at the pictures. Click on the image below to access the article.
Here's some raw film KTRK shot of the 1959 rodeo. Notice there are several additional clips in the row of thumbnails below the video window, including video of trail rides. I recall several of my friends riding in one of the trail rides. I also recall seeing a couple go through Sugar Land on Highway-90A.