Hey, sweetie in the cute boots, the reason your feet are cold and wet and you're slipping is that your boots are stupidly cheap. I know you're a starving student, but maybe next year, you could invest in some practical boots that are waterproof and warm. Put some money aside, watch the sales, and please take care of yourself. Cold wet feet are the worst, and I feel bad that you're hurting and miserable.
Also, tell your boyfriend to stop whining about how cold it is and wear a real coat instead of his gray hoodie.