Not quite. The orthodox Trinitarian doctrine states that God is one by nature (ousía) existing in three persons (hyposthases), namely the Father, the Son and the Holy Spirit.
In other words, one is what God is, while three is who God is.
Given the distinction between nature and personhood, every single person of the Trinity is God. The Father is fully God, the Son is fully God, and the Holy Spirit is fully God. They are not three different gods however, because their division is only due to them being different persons, but they share the same, unique divine nature. So, this is what those among you who say that Father, Son and Holy Spirit are "pieces" of God got wrong.
What about the ice/water/steam example? This is an example that has been used in history, but not to describe the Trinity, but to describe an ancient heresy called modalism/sabellianism. It claims that God is only one person who changes its "modes" over time. In substance, God was the Father during the age of the Old Testament, the Son during Jesus' life, and the Holy Spirit after Jesus' resurrection.
This is not the Trinity however, because under a Trinitarian theology Father, Son and Holy Spirit are not "modes" who change over time, but real persons who share one divine nature.
Dude, we've never interacted much but I'm fairly sure that you are too smart to use one-liners and non sequiturs just to discredit an ideology or a worldview.
Because conversely, I am reasonably certain that the arguments you would present if I asked you to justify such a heavy accusation are a far cry from being strong once you scratch the surface.
