If you wish to have these mobs stay with you then you will need to rename them with a tag. That goes for ALL passive mobs which includes horses. Make sure that you protect your animals in secure areas if you do not want any harm to come to them.
What happens when you right click on a horse with a name tag, are you sure the name tag has a name to it. if you are just getting on the horse or similar try Shift+right clicking.
I had the same issue. You need to use an anvil and set a name or get someone with anvil access too. Once you have a named tag, simply right click on your horse and your done. You will know its complete when the name you created using the anvil shows above your horse. Hope this helps you.
I was shft clicking an normal clicking. Shft clicking brought up inventory, and clicking mounted. I'm going to try the anvil and see. Thanks everyon.
Could you please explain what naturally despawn means then? I have one horse with a name by someone else I have not renamed - do I need to make my own tag for this? I also have three other horses that have never been tagged - Am I going to lose them if I do not put a tag on each one? How long do I have?
