2007, in Romania [1][2]. More specifically, horse-drawn carts were banned. From what I can see, the movement to ban them stems from an argument that horse-drawn carts/carriages are a form of animal cruelty [3]. I haven't seen anything that singles out/bans horses (with riders, rather than carriages) though.

[1] https://www.forbes.com/sites/nadiaarumugam/2013/02/14/the-ro...

[2] http://www.telegraph.co.uk/news/worldnews/1578965/Horses-lef...

[3] https://www.peta.org/issues/animals-in-entertainment/horse-d...