To go for it, you will need to overcome the urge to stay in your comfort zone. Here the comfort zone is tangible: it is your bed, or at least the warmth within it.
If you manage to put yourself in such an uncomfortable situation as a cold shower, you will also remind yourself that you are strong. Such a confidence boost first thing in the morning is definitely a good thing.
With strengthened mind, you are ready to make real progress during the day. A shower is better than coffee because cold water is an excellent energiser for your body.
A natural response to freezing water is to start breathing very deeply. By doing so, you are waking yourself up. Add to this the adrenaline rush from the momentary stress and you have the perfect morning boost.
And best of all: you are going to feel invincible when you emerge from the bathroom.
The best thing about cold water is how you feel once the shower is over. You are fully awake in just a few minutes and prepared to face the whole world.
Furthermore, your mind is focused since it is not possible to have any other thoughts when you are freezing in a shower. In short, after such a shower, you will be alert and ready to go.
-jk-