My friend just asked me this question, and I have no idea how to answer. I have no experience with horses younger than 2, almost 3 and I had always just heard don't ride until they're 2 and even then only lightly until they're better developed, blah blah blah, things of the sort.
So, I told her I'd ask my friends at the HF!
She acquired a filly and has been in the process of desensitizing her. She is about 7 months now. She is so impressed with her progress and how calm and tolerant she is that she put her granddaughter over the fillys back (while holding her to support her weight the whole time, and for safety too) and she did perfectly. Didn't bother her at all. Her granddaughter is about 4. She is wondering if next summer, when the horse is about to turn 2 and her granddaughter is 5- June, July-ish... if it would be safe for the horse to put her granddaughter on her in walk - trot lead games?? She's most concerned about if the horse would be safe carrying less than 50lbs