1) He is my master might work, in episode 11 Takami will be riding a horse, I don't really remember it as a small horse but it is being ridden by a kid so...
In Un-Go Rie Kaishou rides a horse a lot but it is not pony.
I also have a girl riding a stuffed anteater if you want something really odd.
2) Papa no Iu Koto wo Kikinasai! will work, episode 11 will have Hina Takanashi practicing for her daycare's music recital of twinkle twinkle little star. and the performance of it will be in episode 12.