I think it would work with pretty much any type of cord. The only thing you might think about is the pounds of pressure that the rope will withstand. With an old horse who ties like a champ and never pulls back, you can get away with a lighter rope. However, if your horse is a poor tyer and pulls back, you would want a much heavier rope. I have one for Dobe that is made of rope approx 1/8 inch diameter but it is easily broken and only has a weight limit of like 60 pounds. I don't exactly know what Paracord is or how heavy a guage it is but so long as it is strong enough for how well your horse ties, I don't see why it wouldn't work.
Also remember that the smaller the rope, the more bite it has and makes injury more likely if they fight it.