Frozen brake lines from rain

This problem is somewhat counter intuitive solved by using the brakes more than nessesary. You should use the brakes so that they tear down the ice on the rim surface. As the rims are icey the brake performance are poor and therefore not stopping the bike. But it does come with a bit of speed penalty, so it is best to clean the surfaces by breaking at select places on the path you are riding. Downwards is of course a good place to break (even if you doesnt have to lower your speed) and you can pedal as a counter act to the resistant the braking cause. Apply the break force with just the right amount to tear the ice down without stopping the bike. The ice tears down by scratching from the brake pads but also from heat coming from the friction between pad and icey rim. On the flats a gentle brake force for a while can reduce the ice significantly. Do not use any lube or similar. Clean the rims with alcohol or equivalent and use the best brake pads you can find. The pads are not overly expensive compared to the crusial job they are supposed to do, so go for the best!