What type of brakes is least subject to failure in the winter?
Like the other answers, disc brakes are the only way to go if you plan on your brakes getting wet at all. After riding disc brakes for a while now, I will never go back, even in good conditions. I would also really recommend hydraulic disc brakes over mechanical ones, especially in poor conditions. With hydraulic brakes, you don't have to pull as hard to get the same amount of stopping power.