My daughter is past sitting on Santa's lap now, but when she was younger it wasn't until she was about 4 that she was even willing to go up to Santa...and only a certain Santa. I have pictures of my very unhappy daughter with Santa for too many years. But I also have some very sweet pictures of her with the Santa that she loved. She never did tell Santa her secrets though.
I think it all really depends on your child's personality. Every kid is different.