I personally don't think that there will be less horses produced.
Most people don't think that breeding "their horses" will contribute to the problem, as they think they'll always have a market for 'their horses' and think its everyone elses horses thats the problem. So now you have 50,000 breeders or more thinking the same thing. "Its not my breeding program contributing to this"
And then there are the ones that think its cute to have a foal or two around every year, spoil it, can't do anything with it, then get rid of it cause they can't control it. It was fun for the moment, but now its not small sweet and cute anymore, but thats ok we'll have a new foal or two again next year.

Unfortunately people only think in short term and don't think about the impact years down the road much less the horse itself.