If the pony met the height requirements for minis, you'd want to register it WCMHR mini. It wouldn't be able to show in sanctioned A/R shows without A/R papers, but could show in open shows.
If the pony doesn't meet the height requirement and is registered WCMHR show pony, it would be over-height for open mini classes, but could show in other open horse show classes.
Clear as mud? LOL
My WCMHR pony will show in the open horse show at the fair in "Other Light Breed" Class. This puts us in the ring with any breed other than Mini, Arabs, QHs, "Color Breeds" (APHA, APhA, Pinto, etc.), draft and long-ears. The last open show we did, we showed against TBs, Saddlebreds, NSHs, other ponies (Welchies, POAs and QPs) and some other unidentifiable-to-me horses. Some open shows offer classes just for ponies. There are also Pony Clubs and other type of saddle/driving clubs that WCMHR papers may get her into. Oh, and WCMHR shows of course.