IIRC, they would just grab Storm Cat from the field, let him do his business and turn him back out- he was much easier to handle that way coming directly from the field rather than taking him from the stall for his dates. Not exactly the same thing, but still not the usual way that most farms do it. Winstar shines up their stallions like copper pennies before they bred.
"I reject your reality, and substitute my own!" Mythbusters