I would say that by 3, children have clearly developed personal will. By this time, they have encountered many adult choices and rules made for them, and it is only natural that they soon become aware of what they want or would prefer. Examples of this can be found in eating, sleep times, and preference in play activities.
I believe children initially enjoy supervised structure and a sense of parents being within sight, but that changes as they feel a sense of being supervised or controlled too much. Day care might be one of those things which has a feel of external control not necessarily of their own choice.
And so it is important that children experience episodes of freedom where they are allowed to pick their activities and allowed to play on their own at times within that freedom. Generally, if kids choose an activity like reading, it can be happily be done with grown-ups, but it is best if it is their choice of books from whatever is available. This is also true of collaborative play such as with crayons, paints, play-doh. These possible activities can be made available to children, but it is always best if they choose if they want to do these or something else.
When an adult plays with children or has a conflict with them at this age, the adult experiences, periodically, their will, as in “This is what I want” and sometimes “This is what I need” (in more aware children). For them, there is nothing more frustrating than in not being understood when they speak. That and the abrupt imposition of will by a grown-up out of the blue are often natural sources of conflict.
The best parenting I’ve seen in these collisions of will occurs when the parent gives the child choices as in “You do this or this or this”, then letting the child decide. That approach, if done early on, gives children a more supportive sense of choice and support for personal will and preferences. especially, when one of the choices is “We’ll just do what I (the adult) want or think is necessary.” Children will nine times out of ten pick one of the other choices that reflect their interests or selected whims of the moment.
Ultimately, toddlers can be as self-willed as adults, and, like adults, they make choices just like ‘the big people’. They are that developed, that early on. Something there is that longs for personal freedom and its accommodations at and from a very early age.