Yes they do, do it. I don't think it's as common as it is in bigger horses though. It's fairly difficult and pricy. One downside too is that supposedly its not worth keeping a collection of semen on hand. Most miniature registries won't allow you to register a foal if the semen used is from a deceased or gelded stud. Which I think is silly.
You could always train the stud to ground collect if you don't use a phantom. Posted via Mobile Device