I have the first AMHA registered horse that resulted from an AI breeding. He was foaled in 2001. For quite a few years (and he still may be) he was the only success story of shipped semen. As I understand it, many of the farms who permitted their stallions back in 2000 gave up within a couple of years. The overwhelming reason was the shipping quality, or lack thereof. This is not unique to minis. Several other breeds have difficulty with either fresh or frozen semen. I know of several farms who tried experimenting with different extenders with limited results.
Mountain Meadows is right. AI expenses are not for the faint of heart, or pocketbook. My total expenses - not including a stud fee (collection, shipping, insemination, ultrasounds, farm calls, etc) was $2400. In hindsight, I never would have done it had I know the expenses would have climbed so high. At the time, however, the mare was holding on to an increasingly large follicle. The choice was was to stop calling for additional shipments, or continue on. I opted to complete just once cycle. I am just lucky that she caught the first time around!