Its an optimization issue with the standard tiny amount of lag that is the 'internet' in general. The way the code tries to calculate were the horse is at on a multiplayer server and then calculate were you are at takes twice as long for it to just figure out where you are at so it lags trying to keep up. It gets even worse when you are trying to lead other horses or animals with a leash while riding another horse.
My normal ping is around 80 which is rather low considering i'm in america and playing on a server based in germany, I get no lag movement while dismounted and just running around, it only starts when I get on a horse, and then ends as soon as I get off the horse and it is only in relation to the horse moving. It also seems to work find when going backwards which makes me think it has something to do with the way the game calculates horse movement and trying to upload/download that to the server which is the problem.
On a single player game where there is no upload/download lag, horses work perfect fine, except for all the other issues, like their massive hit box, and the way they need to inhabit the very same block as you when you are using a leash on them...
Current version as of March 7th, sorry don't know exact version. I built 3 iron golems in my mountain fortress.
One was in a hallway 5 wide and 12 high surrounded by about 20 doors with 6 villagers living in the area.
Two was spawned in an unpopulated intersection of tunnels approx 12 wide and 12 high, medium monster spawn rate area.
Third was spawned in an open clear grassy area in the middle of my outside area of my fortress with almost zero mobs ever spawning near it, he just wandered around the yard like a good golem.
Two disappeared first about about a day or two real life time, I figured he died which would be odd because mobs don't spawn when your not close enough for them to spawn and I hadn't been over in that area in some time.
Then the Third disappeared but this one was weird. I came out the main door of my fortress and I literally seen the pumpkin block and an iron bar in the air where the iron golem should of been and then it dropped to the ground but right before it hit the ground it disappeared too. I ran over to try and salvage the iron but it was already gone. There was no hostile mobs anywhere to be seen in any direction, and it is a pretty well lit and secure area. The only other mobs around are pigs, cows, chickens and some horses, but they are all securely locked in barns and stables far removed from the golem.
Then Finally the First one despawned, he hung around the longest in the hallway with the actual villagers, no monsters ever spawned in the hallway either it was to well lit.
I'm assuming this is either an issue with the game trying to put the golem back when you been away from it for quite some time, like horses and tamed pets, some glitch causing them to despawn into their base components instead of reform as an actual golem, or maybe their is a check in their AI to seek out the village and when they can't find one and it doesn't have enough villagers they get confused and fall apart.
Either way this is highly aggrivating when you play in survival and take the time to make some golems to clean up trash mobs like zombies from your area and they just despawn and fall apart. I can say without a doubt 2 of my 3 golems just despawned, fell apart, failed to reload, the third probably did the same but I didn't observe it enough to say 100% what happened to it.