Green cross - suitable for the current class but higher leve that your current
Red cross - not suitable for the current class
Color spot - indicate the actual color of the item which might differ from color shown on the item's icon (lets say white hat with red spot will indeed be red when equipped).

Each item has the class(es) or group of class specified in the item description for which it is usable so you can see that before picking it up as reward or purchasing. The material it's made of is irelevant to this. If the item doesn't list Archer or DoW group that it can't be used by your Archer character.