I think it depends on the nature of the individual horse, what kind of clip you plan to do, etc. I don't think I'd full clip a youngster, but that's personal choice. I live in New Zealand and my horses are double rugged (they live outdoors) for a good two months of winter... and so to clip a youngster would seem wrong in my books! As it is, our show season here is beginning and I've only just taken my horses down to one rug (yes, I'm a tad over the top, but I blame that on bad habits picked up from my show queen of a friend lol) and if I were to clip my gelding right now, I'd have to double rug again... so I'd also play rugging into a factor and with youngsters I wouldn't wanna be over rugging them lol.
I'm babbling now, so my basic answer is... what the plans are for the horse, the individual nature and what style I was clipping for, would all be a factor in my decision as well as on the rug factor. Naturally people with barns, etc wouldn't have as big of a deal as I would!
I guess it really depends on why you want to clip. I have a weanling that was first clipped when she was 4 months old, just the muzzle and ears (for show). Two weeks ago she was given a full body clip (for show reasons). We started working with clippers from the day she was born. We would run the clippers all over her body (not the blade but the handle).
It can be done at any age, you just have to be prepared to keep them blanketed etc if you do choose to clip them. I only start doing it during the winter due to heavy riding and during the showing season. The rest of the year is just to much of a hassle.
You can clip a horse at any age, but your going to teach them what the scary loud clippers are at a young age. This would help because when they are older they are alot stronger and you could get hurt if they freak out.
I think that age is not important but the horse should be well handled and used to wearing a rug as well as loud noises and being groomed all over, otherwise it may be dangerous!
For more help on clipping, theres a really good video showing how to do clipping step-by-step, on a site called HorseHero (i'm sure it'll come up on on google) if you get to the horse hero site and search clipping it'll come up :)