I would say maybe 3-4 or more years. Why do I say that?
You start them at 17-18 months old. And that is 2- 2.5 years of training before the futurities.
Then it takes 3 years before they are "finished" where you don't have to worry about keeping them at a trainer all the time to stay winning open or nonpro.
I wouldn't call a cutting horses finished until it had a year or 2 showing under its belt.