I have been wondering, is there such a thing as being too attached to your horse? How do you know if a person has a healthy attachment compared to an unhealthy one?

I think it can be healthy as long as the horse/s and yourself are properly taken care of. Are you missing work to play with your horse, does that relationship take priority over other things that need to come first, that type of deal.

I should think it would take some pretty warped thinking to develop an unhealthy relationship with any animal. I would think that a person would have to be extremely depressed first and hopefully someone near the person would intervene.

I should think it would take some pretty warped thinking to develop an unhealthy relationship with any animal. I would think that a person would have to be extremely depressed first and hopefully someone near the person would intervene.
I completely agree, which is why I want to know so that if anyone is having an unhealthy attachment I will know and be able to get help for them.

I think if things that are more important are being replaced with the horse, and if the person is spending all their free time with the horse, then I think it is unhealthy.

While what you have already mentioned falls under unhealthy (just as it would with a romantic relationship oftentimes) you also need to remember that someone who does not put the horse's well-being above their own wants and desires is also unhealthy. While you may love your horse and feel like it would only be best with you, oftentimes emotion clouds your judgment. If you cannot properly care for your horse, including food, vet checks as needed, exercise and room to run it may be better off with a new owner.