{T}: Add {C}.
{3}, {T}, Pay life equal to the number of colors in your commanders' color identity: Draw a card.
Color identity is set before the game begins and doesn't change during the game, even if your commander is in a hidden zone (like the hand or library) or an effect changes your commander's color.
If you don't have a commander, you can't activate War Room's last ability at all.
If your commander has no colors in its color identity, you pay no life to activate War Room's last ability.