Indeed :) I found out both of these things when I was trying to research TWHs - and so I thought the idea of having a TWH in the plot was over (Originally I came up with the idea because of course she's older so she might prefer a gaited horse lol more comfortable - I found out that's one of the top reasons TWHs are reccommended for older people because they're more comfortable and less stress on that person's joints).
So when I found out that the registry wasn't created until 1935 and etc I thought that plot idea was done. However, I also realized I had another character who came from the American south that likely would have seen TWHs and would know a little about them as he was raised in farm life, who also is an acquaintance of the gentleman who bought the horse so could then reccommend if he wanted to find a horse that was originally bred as plantation horses, used to carry people around their plantations etc. - that he check out TWHs - even though they don't have a breed registry. He's not highly concerned with getting her a registered horse - she doesn't want to do showmanship or anything.. he just wants to find her a very nice horse that will be the most comfortable for her to ride and provide her some companionship.
I try very hard to solve all the plot holes so my work doesn't sound silly
but thanks for bringing it up because if I hadn't have known I would have had a hairy problem to work through!