You’re right, keeping horses as pets, for that matter keeping any animal as a pet could be “construed as worthy of ‘outlawing’.

All the pets we have ever “owned” have come to us one way or the other because animals have been kept as pets.  We would certainly never abandon them but likewise we’d never breed them to produce more pets.

The moral argument for keeping a pet is in many ways similar to that of keeping animals for food.  For me, so long as those animals are treated well and killed in a humane way when necessary then I don’t have a problem - others have a different point of view -  if and when they become the viewpoint of the majority then I will abide by that.