Early in Israelite history the Jews were forbidden to make pictures of God because he had not revealed himself to them in visible form. Had the Israelites made images of God, they might have been tempted to worship them, much as the pagans around them worshiped images. God later revealed himself under visible forms. One instance is found in Daniel 7:9-10: "As I looked, thrones were placed and one that was ancient of days took his seat; his raiment was white as snow, and the hair of his head like pure wool; his throne was fiery flames, its wheels were burning fire."
The Holy Spirit revealed himself under two visible forms--that of a dove, at the baptism of Jesus (Mt 3:16, Mk 1:10, Lk 3:22, Jn 1:32) and as tongues of fire, on the day of Pentecost (Acts 2:1-4).
Most notably, God the Son visibly revealed himself in the Incarnation: "[A]nd going into the house they [the magi] saw the child with Mary his mother" (Mt 2:11).
Since God has revealed himself in the above forms, he can now be depicted under these forms. Keep in mind that Protestants have pictures of Jesus in Bible story books, that they depict the Holy Spirit as a dove, and that they depict the Father as an old man sitting on a throne. They do all these without the least temptation to worship these images as God.