By not wearing longs, the blood supply to your feet is cooled that bit more on the way down so the body's ability to keep your toes warm is reduced. In very/extreme cold weather conditions that's why people use 'wrist warmers': to minimise the reduction in the temperature of the arterial blood supply to the hands/fingers. So, with the suggestions above: thicker or even waterproof socks, wriggle room in footwear, boots, overshoes, chemical heat warmers, decent mudguards, deliberate wriggling your toes - medium thickness longs will keep your feet warmer (and reduce the amount of water getting down the skin to the inside of the socks. Leg warmers will do the same job.