Does the Nicene Creed suggest a strict division of responsibilities within the Trinity? In the Nicene-Constantinopolitan creed, the three persons of the Trinity each seem to have their own role in creating the world:


The Father is "maker of heaven and earth, of all things visible and invisible".
For the Son, we have "by whom all things were made", a clear lifting from John 1:3.
The Holy Spirit is "the giver of life" (Greek ζῳοποιόν, Latin vivificantem).


Does this text intend to suggest a strict division of responsibilities (eg, the Father does not give life, the Spirit did not make heaven and earth), or is it more like giving emphasis to the ways in which each person contributes to a single creative will? In particular, what distinction is envisaged between the Father, who makes all things, and the Son, by whom all things are made? My sense is that the authors wanted to make some sort of distinction, but not to the extent of dividing God; I'd like to know how they thought about the ways that the three persons of the one God are responsible for creation.
I don't think the intention of the council fathers was to divide the job/responsibility of Creation between the three persons. Saying the Father does not give life or the Spirit did not make heaven and earth would probably be considered heresy in the early Church.

The Orthodox Church in America states that, "There is no will and no action of God the Father which is not at the same time the will and action of the Son and the Holy Spirit." ... The action of each is the action of all; the action of all is the action of each. And the divine action is essentially one."

Also saying that a person contributes to a single creative will could be understood as saying that the will is not in full control of the person, and that therefore the person executes the will like a robot. Which is also not correct. The CCC 258 sheds more light on this issue:


  For as the Trinity has only one and the same natures so too does it have only one and the same operation: "The Father, the Son and the Holy Spirit are not three principles of creation but one principle." However, each divine person performs the common work according to his unique personal property.


I understand these are not the references from the actual the authors of the creed, but rather current interpretations of their words. But I think they are in union with that of the council fathers. For example the quote within CCC 258 is directly taken from the Second Council of Constantinople.

Then one might ask why the council fathers used this distinction. I assume that they had a very hard time (as we still do) explaining the trinity and that its three persons are distinct persons while having the same will, power, action without sharing these attributes, rather being in full possession of them with harmony at the same time.

In conclusion, all things that are done by God, are done by the Father, through the son, in the Holy Spirit.