I have received the following reply from HRA's Andrew Kelly, the Keeper of the Studbook:

"Regarding the descendent genotyping of horses - our lab informs us that this is far more difficult in horses than in humans and given the current technology, costs involved and probability of an uncertain outcome, if we were to undertake this as a project, then we would be better to wait until the processes were improved (they are continually improving). On balance, we will re-visit at a later time."

So I am afraid we will all have to be patient. If I am still around I will ask again in a couple of years LOL