Let me state this: I'm about to suggest something that I've barely an idea of how it works, but it seems to work!
Will Smith  is the original owner of this suggestion in the Facebook page:
As I suppose you won't update the mod from 1.7.10, could you maybe implement the new thing with making Horses and boats etc Client, as the new update did? Would be really helpfull for servers. I understand if this is not in the priority list thogh.
So, I tested the new 1.9 update with horses and the difference is abysmal. While riding in Middle Earth is a cluncky experience, riding a horse in 1.9 vanilla Minecraft feels like playing Minesweeper in a NASA computer. It was wonderful! No lag, no chunk generation weirdness...
So, I suggest that all types of mounts (rhinos, horses, spiders and etc) be controlled client-side instead of server-side, as it currently is (it would be quite funny if mounts are already client-side in the mod hehe).
It seems to be a feasible thing in mods, because in one of the links I'll provide later in this post, talks about how the dev of the Aether mod made his mounts controlled client-side. And as we know, the horses of the Middle Earth dimension are totally distinct mobs from the horses of the Vanilla dimension, so that means that the horses of ME can be changed to client-side without messing with the vanilla horses. At least I think so, we need a professional opinion.
These are some references for people curious about this whole thing:
TLDR: Horses controlled client-side are less laggy than horses controlled server-side.
In case you don't want to check the links, this is a good explanation of how this client-side/server-side thing works:
This is because, as far as I understand it, the client tells the horse to move, then the client sends a signal to the server telling the server to move the horse, then the server sends a signal back to the client to inform it that the horse has moved and to update accordingly. This results in lag between telling the horse to move and having the horse actually move. When controlling just the player, the client moves the player and then tells the server where the player is now. This way there is no input lag for the client controlling the player. This is how it should be done for boats, minecarts, and horses when a player is in them.
The same thing happens in Singleplayer, because Minecraft runs an internal server.