I have no intentions of becoming a trainer, but here's my story: I contacted a local Arabian farm, telling them I'd be interested in taking some lessons on somewhat greener horses (shortly after saddle broke). They have a small lesson program, so it wasn't a crazy request. They put me on their lesson horse for two lessons, and after that on their broke-to-ride, for-sale horse (Everest). Shortly after, I took him on his first trail ride ever, and I've been riding him weekly since. In the beginning of June, trainer asked me, "Do you want to help me break a horse?", referring to a horse that needs a lot more time than he can afford with all the other obligations on his plate. So I started doing groundwork with that horse, independent from the "lesson" arrangement. And you know you're doing it well if the trainer watches you for 15 mins and then leaves you to it, tending to something else.
So, a breeding farm will have many horses that need to be trained, most of which are straightforward and without special issues, so you can get your feet wet with a "standard" course for a horse. If you volunteer your labor, I can't imagine them turning you down, especially if you are promising enough to turn into a time saver for them after a short while...say you work with a horse in one end of the arena, the trainer with another one on the other, keeping an eye on you.
Worked for me - so for what it's worth. I enjoy it a lot. :)