Piggybacking on nrha and rookie, breeding by AI is easy and relatively inexpensive and requires only a moderate amount of training.
I say this because I worked for a couple of years for a farm that breed all mares onsite (about 40) to two stallions and bred soley by AI. We did not have a vet do the collection of the stallion or the insemination of the mares, we did that with the staff on hand, but we did have the vet come out thee times a week during breeding season to palpate mares and to ultrasound bred mares.
We gave a sweet old gelding a big ol' shot of testosterone and used him to tease the mares, and he did an excellent job while remaining docile and easy to handle.
The special equipment was a phantom, an AV and the "lab" was a tack room with a sink, refrigerator and microscope.
Shipping semen is a whole 'nother deal, with a great deal more technology, expertise and logistics required.
And as nrha pointed out, the key ingredient in that situation is a stallion of such reputation and in such demand that mare owners are willing to pay all the additional costs associated with breeding by shipped/cooled semen.
I confess I don't know a whole lot about embryo transer in horses. I have only EVER heard of it being attempted with mares at the very top of their competitive careers, so I have to assume that it is both expensive and risky.