Well, he certainly was one of the lucky greys... what beautiful, clean-cut dapples! My arabian kind of skipped that stage and went straight to freckles. 15 days doesn't seem like that long for him to rest though, I know very little about OTTBs but that seems a bit short to me.
From bottom up, he has nice, short pasterns with good slope. His canons seem long all around, especially in the back, but his back legs look like they're very correct angle-wise. His front legs look straight enough in the first two pictures, but he looks to be very over at the knee in the riding pictures... I'm not sure what to make of that, I'm too much of a conformational amateur. Maybe it's the shadows playing since his legs are black. His forearm is short, and he looks like he's set under himself. His shoulder is straight (and a bit small IMO), and his neck looks set on a bit low to me. His withers look okay, not too big but still there. He has good depth to his girth. His back looks very short to me, and I think he might have a roach. His hip is nice, although his croup looks really steep in the riding pictures. He's built pretty downhill. Overall, a handsome boy.
I am definitely not an expert in the field of conformation, so keep in that in mind- if someone comes and says I'm wrong, I most likely am. :)
-edit- and welcome to the forum, thank you for sharing your handsome new boy!