What is a horse called if it does not take much attention?

A horse that does not require a lot of attention in terms of not needing lots of special food or constant attention by a veterinarian or farrier (horse shoer) generally is called "an easy keeper".

But don't forget that horses are herd animals and need to have lots of attention from their herd mates (other horses) and lots of care and affection from those who own them.

All horses need a safe environment, access to grass or hay, a constant supply of fresh water, daily attention, and periodic visits from the vet and the farrier.