IIRC, I was able to store horses around 60th circle whenever I was able to start catching them. I'm honestly not sure on the exact number because it was awhile ago for me. There really is no contest or factors to it, the way that Rangers store horses is no different than the way Traders store them. It's just a command.
I do not remember hearing about a limit to how many horses you can store. I heard some talk from Dryzt's player years ago about the herd itself not coming out after you have like 5 vouchers, or coming out less often, but I never verified. I know that I've had up to 4 fully-trained horses stored at once while my own mount was in stable for use.
You're going to get a bad reputation if you go around pinching every spectral reaper you see.
