Wasn't sure where to post this, so I'll start here.
If I were to see a horse on the track that I was interested in, how do I go about approaching its owner/trainer about a sale? Horse isn't on CANTER but was running in a claiming race (which the price was more than what I would have wanted to pay). Is it presumptuous and frowned upon to approach the trainer?
You might have better luck asking on the racing forum, but...if the horse is running in claimers, and not listed somewhere like CANTER or FLTAP, technically, yes, it's "for sale" (in that anyone able to drop a claim on it can.) So it can't hurt to ask. If the horse has been dropping levels and is not bringing in purses, the trainer or owner might be interested in moving it along.
Caveat: When you say "more than you wanted to pay", how much more? If it's running in a $25,000 claimer at Belmont, it's not doing badly at all and has a long way to go before it runs out of conditions. You'd be wasting your time, in all likelihood, if you called up and offered $2500. Now, if he's in the $7500 claimers at Finger Lakes, yeah, you offer $2000, the trainer might jump on it or be willing to negotiate. IOW, don't lowball him.
And I say trainer, but remember he/she might not own the horse, so they would have to run your offer past their owners.
Speaking from experience, I have purchased a ton of horses off the track, literally hundreds.
First thing, almost every horse on the track is for sale, qualifier being allowance and graded stakes horses, and they are for sale too, but the price makes purchasing them as hunter/jumpers a moot point.
In my opinion purchasing anything off the track for more than $2,500 is kind of silly, as there are lots of OTTB's available that have had let down and some saddle time, which makes it much easier to gauge their true potential as hunter/jumpers.
If you do not have access to the trainers outside of simply going to the track, like everyone else betting etc., simply wait until the race is over and ask the trainer if the horse is might be for sale. Every contact I have that runs horses has be created by simply asking.
I would suggest that you do your research however. Get the racing form, check their record, check for changes in trainers, conditions, running gaps, performance anomalies etc., and pay special attention to them when they come back from the track, this is when the story is usually told regarding soundness etc.
And the best advice ever given to me is simply "don't fall in love with them".
It isn't presumptuous at all to approach a trainer. I'd go up to them, casually explain that you are looking for a riding horse, and mention that you like horse X and ask if they'd consider selling it. I don't typically mention showing, because they will expect a higher price. If they are amenable, I ask some questions about the horse's history and soundness, and over the years I've been pleasantly surprised at how honest most people are. Be sure you have cash with you and your trailer close at hand when you shop for TBs in this manner.
Most trainers are extremely happy to develop contacts within the riding horse industry since racing can be a very short career for many horses and it benefits the trainers to be able to move along horses that aren't racing well. I can almost guarantee you that if that particular horse isn't for sale they can and will steer you down the shed row to a couple of others that are. If a horse is for sale but they want too much money for it, I'll leave my name and number just in case.