Yes taking cold baths or taking cool showers can help burn calories and help you burn off fat.
Cold baths or cool showers activates brown fat and when that brown fat is activated it generates heat around the body which helps you burn off fat.
Your body then uses that good fat to create the heat for your body which burns off the fat and burns calories so that you lose weight.
Exercise is also good for losing weight too but the cold baths can help some if you're wanting and willing to take cold baths or cool showers.
Pouring cold water over your body could also help you lose weight and burn off calories as well.