You say horse stall mats but the link says exercise mats. One picture in the HD ad shows interlocking edges but the rest do not. At 0.20" thick, they are little more than a cushion; actual horse stall mats are in the order of 3/4" - 1" thick an stay in place primarily by virtue of their own weight (they are annoyingly heavy). Besides, horses just walk and occasionally sleep on them. I suppose you could try hold or cold set carpet tape; can't hurt. How much they move will, I suppose, depend on what type of exercises you do.