My youngest son is not quite two and definitely wouldn't sit still for a hairdresser or barber to cut his hair. His hair was starting to get too long so I decided to have a go myself. The results on a wriggly child were definitely not good and please don't ask me to share a photo.
No, I wouldn't be game. Fortunately my eldest quite likes having her haircut and has sat happily still for the hairdreser since she was about two. She did try to cut her own hair once. It took quite a while before I could put it in a ponytail again because there was a short bit that wouldn't reach.
I cut both my two daughters' hair. But....it's down to their waists, all one length. So, it's very easy to just trim a little bit off the bottom to keep it neat and tidy. I wouldn't trust myself enough to do it if it were shorter.