

I was going to Meiji Shrine (明治神宮) yesterday and so got off the train at参宮橋駅 on the Odakyu line. As I was walking to the shrine I noticed another horse park with people taking riding lessons and also children being given the chance to ride ponies.
After further inspection it turned out to be Tokyo Riding Club 東京乗馬倶楽部 (website here)
It is a club but you can also go there as a visitor. Prices range from about 7,000yen for a 45 minute ride on a horse to packages for a number of lessons within a given time period.

Of course you could also just ride a pony :-)