Cold is what makes people think twice, or not at all about doing a dogsledding winter trip or any winter trip. But cold is also an unexpected treasure. The first time it drops below zero, every single year, I procrastinate going outside, and inevitably I over prepare. I end up outside sweating, feeding dogs at -20F and wondering what the big deal was all about.
When you dress well you can overheat quickly. But it also helps when you go out and stay out. When you travel from a warm house to a warm car and back again you are going to freeze. Getting out in the winter and staying out can expose you to a world both outside your self and inside yourself.
This was express very well by Calvin Rutstrum in his book Paradise Below Zero:
With an animated state of body and a new outlook, it is difficult to understand how one could possibly have held the sluggish indoor point of view about cold and snow that was coddled earlier. It is also equally difficult while bogged down with the lethargy of long, physically debilitating hours indoors to understand how one can have the invigorated state of mind and body one now possesses outdoors after the first mile or two of activity and climatic adjustment.
In other words get over your fear of the cold and get outside the water is fine.