Since the cost is still out of the realm for most, I think that will give time for people to evaluate the success of the clones already done - like Sapphire's. If those clones are "as good" or better as the original and the cost comes way down, there will definitely be an increase. That is also with the caveat that there is no decrease in longevity or health issues with clones.
I saw there are a large number of polo ponies being cloned in Argentina (I believe that is the location), so there is a large pool of clones to study plus the sport horses that have been done here.
There will always be a need to make new and keep genetic diversity alive as well as a large number of people that want an "original" and want nothing to do with clones.
Irish Draughts and Irish Draught Sport horses
They have a Quidam clone somewhere but I haven't heard anything new on him. Any Olympic horse, or TOP breeding stallion no longer producing (Baloubet, Quidam, Darco, etc), or who has always produced horribly (Berlin, etc) should be cloned in my opinion.
Too much expense and too much controversy for now so the answer to the original OP question is IMHO No , not for a long time or ever will this influence stallion owners and fee's much at all. It could bring in genetics not available prior to cloning but outside of that, most breeders like to go forward and see progress in breeding not go sideways.