It appears these were sold in the 1950s and 60s.
Photo of real ones.
Youtube video which shows a few shots of them in action, but it's not the exclusive focus of the video.
It wasn't a proper tobogganing day if at least two of us didn't land on our coccyx¹ and agonize in the snow, incapable of breath for an absolute eternity of 30 seconds of recovery.
From atop the hill you'd watch your mate take a hard landing on his back or hind after hitting the hump that you all tried to steer away from, and see him writhe, gasping soundlessly, knowing exactly what he was feeling, thinking, and praying, "not me, this time, please, not me." And then you'd take a running start with your Crazy Carpet down the exact same path.
- While researching for this comment I learned that the condition "getting the wind knocked out of you" is called phrenospasm, caused by sudden impact to the chest/trunk, which jibes with a hard landing on one's back. It is not, as far as I found, related to impact on the tailbone, but I am posting this comment as writ. because, well, coccyx and I am a 55-year-old child.