The Creed as promulgated at the Council of Nicaea was actually very short, and didn't include the "worshipped and glorified" phrase:
We believe in one God the Father all powerful, maker of all things both seen and unseen. And in one Lord Jesus Christ, the Son of God, the only-begotten begotten from the Father, that is from the substance [Gr. ousias, Lat. substantia] of the Father, God from God, light from light, true God from true God, begotten [Gr. gennethenta, Lat. natum] not made [Gr. poethenta, Lat. factum], consubstantial [Gr. homoousion, Lat. unius substantiae (quod Graeci dicunt homousion)] with the Father, through whom all things came to be, both those in heaven and those in earth; for us humans and for our salvation he came down and became incarnate, became human, suffered and rose up on the third day, went up into the heavens, is coming to judge the living and the dead. And in the holy Spirit.
What we commonly know as the Nicene Creed was included in the record of the Council of Chalcedon (AD 451) as having been promulgated at the First Council of Constantinople (AD 381). It's also known as the Niceno-Constantinopolitan Creed:
We believe in one God the Father all-powerful, maker of heaven and of earth, and of all things both seen and unseen. And in one Lord Jesus Christ, the only-begotten Son of God, begotten from the Father before all the ages, light from light, true God from true God, begotten not made, consubstantial with the Father, through whom all things came to be; for us humans and for our salvation he came down from the heavens and became incarnate from the holy Spirit and the virgin Mary, became human and was crucified on our behalf under Pontius Pilate; he suffered and was buried and rose up on the third day in accordance with the scriptures; and he went up into the heavens and is seated at the Father's right hand; he is coming again with glory to judge the living and the dead; his kingdom will have no end. And in the Spirit, the holy, the lordly and life-giving one, proceeding forth from the Father, co-worshipped and co-glorified with Father and Son, the one who spoke through the prophets; in one, holy, catholic and apostolic church. We confess one baptism for the forgiving of sins. We look forward to a resurrection of the dead and life in the age to come. Amen.
The Greek phrase in question is τὸ σὺν πατρὶ καὶ υἱῷ συμπροσκυνούμενον καὶ συνδοξαζόμενον (to syn patri kai yio symproskunoumenon kai syndoxazomenon). It's the sym-/syn- prefix which is translated as co- in the version above. -μενον appears as the suffix for the present participle passive form for verbs that have infinitives ending in -ειν. Thus συμπροσκυνούμενον means "is being worshipped together".
Because it's a passive form, there is no defined subject — that's what the passive voice is used for, even in English. It's the current state [of being worshipped and glorified] which is important, not who is doing that.
If I were pressed, I would posit that it is the whole Church — militant, expectant and triumphant — which is doing the worshipping and glorifying.