Most people will be scared and it's normal. That's why it's important to train your body before the actual plunge in cold water. You need rapid exposure to the cold temperature. Usually it's done in a shower when you pour a bucket full of cold water on yourself starting from the head, which is important. This is done after your usual shower. The procedure is followed for at least several weeks and usually during autumn so that later on you can start running barefoot and quickly rub yourself in snow. After that you can proceed to swimming...
Cold water and winter swimming in particular has a very potent spiritual effect when your spiritual body (or astral body) loses karmic relations or negative energetic attachments to the astral body. Putting it simply - the applied rapid cold in our physical world results in the opposite in the spiritual world, which is rapid heat, and vice versa.