What a cracking idea. I'm 100% certain daughters pony would walk in happily, it would only be a 40min hack to one too. If security objects, I will of course just point out that horses are allowed as they stock them.
The reason I'm certain daughters pony would go in is cos she actually attempts to follow daughter in anywhere. She's been in houses, & has been forcibly restrained from following daughter into a pub, McDonald's, shops & a few other places. Including trying to get in a portaloo with daughter at a show. The co-op we pop in for choc & drinks on the way back from one ride she's made frequent attempts to get in, so I have no doubts she'd march into tescos.