I think there's a difference between already having a horse/pony there in the paddock, than specificially going out and finding one to buy for the child ITMS?
My mum had an old horse when I was little, I don't remember much but I can bet I was up on his back occasionally. I didn't actually get my 'own' pony until I was about 7 or 8 (and after the first nightmare we got, the little paint pony we ended up with was just a darling, seriously the best first pony EVER!).
I think they should at least be able to say "i'd like to learn to ride" or something to that effect. At 1 I dont think they would really understand, and while they might not mind sitting up on a big horse there's a difference between that and actually riding on your own. I don't know how she could even be bothered, with DD I know I'd spend 20 mins getting the pony ready to ride, put her up and have her wanting back down on the ground 10 seconds later!