My just-three year old likes to hold my hand, but doesn’t have to. I do tend to walk on the outside of him, but I trust him not to run into the road on purpose - I worry more about freak accidents like him tripping up and falling under a bus.
He goes ahead of me on his balance bike on quieter roads, and we have done a few trips to the park (along vv quiet residential streets, people often walk down the middle of the road in one of them) where I ride my bike on the road and he rides his on the pavement next to me. He knows to stop at kerbs.
In the park, he needs to stay in sight but can play hide and seek, hide in bushes, and go ahead of me. I have been encouraging him to go and put stuff in the bin in sight of me but a little way away, to get him used to doing little errands on his own.
He likes to explore but usually he likes to explore with Mummy, so he drags me with him rather than running off. If he was a bolter, or didn’t stick to me like glue through choice, I’d probably give him less freedom.
By the time he starts reception (18 months), I would want him to ride or scoot to school with me walking alongside, to play in a playground with his friends with minimal supervision from me (at the minute I get dragged round with him to join in his games), and to be able to go to the ice cream kiosk or similar if I give him the money and watch from a distance.