The fuck? Templars were known to wear white capes with their plate armour.
In the time period the templars were a big thing, they didn't have plate armour, so no. Maybe parade armours in later periods for the grand master but not for normal men at arms.
EDIT: Capes are things people would wear on a daily bases, but not when going into a battle. A cape would get in the way a lot and if you want a cape to protect you from rain and cold, which is what they were used for, they'd need to be thick, so heavy. Extra weight kills you in battle.