Measure him. I haven't even looked at the picture, but there's no way that I would be comfortable judging any horse's height without a point of reference unless I was in person. Use a measuring tape, and get a buddy to help you hold it while you read it and you'll get a much better idea than asking anyone on the internet!
I'd have guessed 14 hands without knowing your height too, but given you're 5'3 I'd put him closer to 13 hands because he's a fair bit shorter than you. He is going to grow though, just measure him when you go out next.
He looks to be about your shoulder height, so just look through pictures and find out where he is up to on you, and then measure from the ground to your shoulder or whatever to find his height.