Not exactly the same but howrse is a horse browser game

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There is "Wild Horse's Valley " it has a similar idea but different mechanics, with lots of things and colorful horses to explore :D

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I played Howrse for years before playing Lioden (I lost my acc info sadly, RIP to all my pegasi and unicorns). It does rely a bit more on in-game currency, but I think my favorite thing and the most similar thing to Lioden is the events they had every month.

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Seconding the above that Howrse is probably closest to Lioden (although still not super comparable). Although, my personal favorite is Horse Reality. It is a lot slower paced than Lioden and has a smaller player base. It is supposed to be more "realistic" so no unrealistic colored horses, or fantastical items. You get to focus more on breeding for stats or competition. I understand it's probably not for everyone, but I enjoy it a lot!

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there's equiverse, which is made by Abbey and is very similar to LD, but it's pretty old and the community isn't super active

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Indomita is simillar on the sense of playing as a wild animal, breeding them for color on a fantasy world. It's been a while since I played it, but from what I remember, the fun of it is more on loring your characters and interacting with other players. It was a bit deserted, but at least it had coat genetics.
World Of Ravalon has a exploring system a bit simillar to Lioden with the encounters, item collecting, and quests about giving items to npcs, but you can't breed the horses. It's a pretty small so the players may not feel very active tho.
Khimeros is not about horses, but has equine species in it. The breeding is simillar to Lioden with non-genetics inheritance and the focus on breeding projects and dressing up your pets.

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