Does everyone get to see the color of a train card drawn from the pile?
No, when you draw a card from the deck it is hidden to the rest of the players. Other players only know what you get when you pick one of the face up cards.

One of the benefits of drawing from the deck is others don’t know what you get but you also don’t have a choice of what you get. Another possible benefit depending on the version is the ability to draw a wild card from the deck and get another draw afterwards.