My DD has soooooooooooooo much hair, it is thick and quite curly, she is 3 1/2 and has had about 6 or 7 hair cuts already. I actually have to get it layered to stop all the ends tangling together. I would like to get it cut short, but she has a double crown and her fringe grows forwards, so to make it work, I am pretty sure it would end up looking like a mullet.
Good luck with the hair cut, it usually does wonders for thicker hair.