He's extremely skinny, his coat is absolutely rank [by the way that really doesn't sound like enough... my TB is a very easy keeper, for a TB, and she's getting more than that! free choice hay is great but TB's just don't do well on just that and that little grain, they need more].. if he's only "due" to be trimmed you BADLY need a new farrier because those feet are disgusting and it's NOT "TB feet"... a TB foot is only as bad as its farrier, except that some bloodlines tend to want to throw bad internal structure and there's not a lot you can do about that... I don't mean to be nasty but I see a severely neglected horse.
"He's a hard keeper" is NO excuse for a horse to be in that condition. EVER. My neighbour's horse is a hard keeper and he was in magnificent condition when they bought him... skinny NOW, because they, like you, either don't know enough to, or can't be bothered forking out the cash to, feed him enough. My friend's horse was FORTY YEARS OLD, a hard keeper even in his prime, had no teeth, and still looked magnificent up until the week before she put him to rest.
A horse is never that skinny with an owner who actually cares, unless it has an underlying issue - in which case he needs a vet and bloods done if he has no ulcers.
Most of all, do NOT ride this horse, or ANY horse, in this condition. It's cruel.