I am no expert scientist on this issue. I have been studying gardening and have a few thoughts that may help explain why this is NOT a good idea.
First, we know that "Dolly", the first cloned animal (sheep) was cloned from an old sheep's DNA, and was old at birth, and did not live long. A cloned QH would have to be bred ASAP. If it is a mare, we know that breeding older mares isn't a wise thing to do. If it is a stallion, not so much a problem.
Secondly, if we compare domesticated vegetable plants to domesticated animals, the "heirloom" varieties, which have been bred for taste AND hardiness and disease and pest resistances, duplicate true. Hybreds do not. In fact, if you save the seed of a hybred, you might plant it and grow the wild version of the same plant! However, heirloom varieties don't produce as much.
Cloning is, I believe, a way of duplicating directly a valued animal. Someone would probably want to clone horses like "Secretariat" to produce another big money maker. If you are successful at this you essentially
"cheat" the system. You will also reduce the gene pool. When I re-read "Secretariat" the author spoke of his gene pool as diverse--no in-line breeding, and that even in the 1960's TB breeders knew that their shrinking gene pool was a self-made problem.
I hope that they are not successful. IMHO QH's are about the best breed of horse bc the gene pool is wider than the rest, and other breeds have favorably contributed to it. I hope that this doesn't ruin it.