You could try this! I asked around wondering about my baby and this was cool! We will see if it's right though...
You can do the string test. Take a string and hold it up to the top of the front leg. Then take that measurement and move it up so the bottom is at the top of the leg and the top of the measurement you just took is where the horses' whithers will be when they are full grown. At least I think that's how it works.
Actually a guy did this to my horse and it looked as if he was going to be a 15.2 hand horse it's just hard for me to beleive he will get this tall but the guy told me to just wait and see because he truly beleives in this guess time will only tell though you are only the 2nd person who I have heard to know about this Thanks for your reply!
The best measurements I could find (at least it worked for me). Measure front leg from knee to the coronary band. If it's 15 inch - horse will be 15 hands, 14 inch - 14 hands etc. Better to do after they are 2 years old. I tried it on number of horses for interest (including mine) and it worked very precisely.
Somehow other test described didn't work for my paint. She has very long legs, so the test gave something like 16 hh. She's 15 though and not going to be any much bigger. :)