Early in its history, Israel was forbidden to make any depictions of God because he had not revealed himself in a visible form. Given the pagan culture surrounding them, the Israelites might have been tempted to worship God in the form of an animal or some natural object (e.g., a bull or the sun).
But later God did reveal himself under visible forms, such as in Daniel 7:9: "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." Protestants make depictions of the Father under this form when they do illustrations of Old Testament prophecies.
The Holy Spirit revealed himself under at least two visible forms—that of a dove, at the baptism of Jesus (Matt. 3:16; Mark 1:10; Luke 3:22; John 1:32), and as tongues of fire, on the day of Pentecost (Acts 2:1–4). Protestants use these images when drawing or painting these biblical episodes and when they wear Holy Spirit lapel pins or place dove emblems on their cars.
But, more important, in the Incarnation of Christ his Son, God showed mankind an icon of himself. Paul said, "He is the image (Greek: ikon) of the invisible God, the firstborn of all creation." Christ is the tangible, divine "icon" of the unseen, infinite God.
We read that when the magi were "going into the house they saw the child with Mary his mother, and they fell down and worshipped him. Then, opening their treasures, they offered him gifts, gold, frankincense, and myrrh" (Matt. 2:11). Though God did not reveal a form for himself on Mount Horeb, he did reveal one in the house in Bethlehem.
The bottom line is, when God made the New Covenant with us, he did reveal himself under a visible form in Jesus Christ. For that reason, we can make representations of God in Christ. Even Protestants use all sorts of religious images: Pictures of Jesus and other biblical persons appear on a myriad of Bibles, picture books, T-shirts, jewelry, bumper stickers, greeting cards, compact discs, and manger scenes. Christ is even symbolically represented through the Icthus or "fish emblem."
Common sense tells us that, since God has revealed himself in various images, most especially in the incarnate Jesus Christ, it’s not wrong for us to use images of these forms to deepen our knowledge and love of God. That’s why God revealed himself in these visible forms, and that’s why statues and pictures are made of them.