you can play as a horse in the IT server Dawn of Eternity!
(https://photos-2.dropbox.com/t/2/AADU58m1Q_xIXFoxE2PzzgHc4tBhwYBMhYDZzhwKa-b6gA/12/64467845/png/32x32/1/_/1/2/dawn_of_eternity06122018_141128077.png/EKTAgDIYhAkgBygH/3T3gldEAp-w3vIL1aJSbX8AV26kIZKm1YE3OKNRXTV4?preserve_transparency=1&size=1280x960&size_mode=3)
(https://photos-1.dropbox.com/t/2/AABFWm_OistIL2mjz0yMzTqCreOwZKtjysKcHxFwUgCNaw/12/64467845/png/32x32/1/_/1/2/doescrn2.png/EKTAgDIYhQkgBygH/XZWNtiBnTpbpvLOuvfHLHNA5h3g0uqnVgG4xLB1j82g?preserve_transparency=1&size=1280x960&size_mode=3)
http://dawn-of-eternity.com/community/
there's Legends of Equestria but it's more MLP than horse. it's free and in open access right now. customization is a bit limited atm but there's a lot of nice looking maps you can explore and quests you can do. i'm not big MLP fan but i personally find it a really fun stress reliever!
https://www.legendsofequestria.com/
there's also Alicia Online. i haven't had any experience with it but it's a korean horse mmo kind of like Star Stable but looks a lot more nicer imo. there's probably a lot more you can do as a free member in Alicia but don't take my word for it.
https://aliciagame.com/
iiiii don't recommend Second Life unless you're 18+. a lot of the worlds are 18 and over only.... for a good reason.
I'm about 3 years too late - but here we go! There is a game called Horse Isle 3, it is a FREE 3D open-world game where you can tame, buy, and breed your horses. It has a heavy emphasis on breeding cool coats, different breeds, and higher stats. I 110% recommend checking it out if you are still interested as it's not super popular - they have also just added donkeys so... yea :)Definitely not a fan of HI3 after their anti-lgbt incident :P
ALsO the first few hours of the game will be tricky as there isn't much of a tutorial and you start completely from scratch - no horses, no tack which means running around on foot looking for a wild horse. So definitely ask in global chat for help starting out. :)
https://hi3.horseisle.com/www/index.php