In theory, it's a good idea. In reality though, many employers in this industry abuse working students more than regular staff, which is saying something. You are often treated like free slave labour and made to work excessively, and in some cases, treated like dirt. As bad as the industry can be to experienced staff, I've found many more employment laws get broke around working students. Of course, they're not all like that but be very careful about who you get your placement with. Tighter regulation on employment of grooms is needed all round. I have found though, at least here, that the racing sector is considerably better than the sport horse sector at treating staff right.
I would imagine that the right age would depend on the country you are in.
You do the same as what everyone else does, except you generally have more supervision and more instruction on how to do things. The idea is that you learn all aspects of horse care and grooming; mucking out, feedings, plaiting, tacking up, clipping, washing tack, washing horses, general yard tidying, possibly lungeing and/or riding depending on experience, etc. It's tough work, even when you are treated well, and can involve early mornings and late nights. In some places, there is also a nightly check that you may have to get up to do. In stud farms, there is usually a night shift during breeding season.