Going outside during the cold weather when you have a cold or flu will not do you any harm. Since getting a cold or flu requires a virus and is not contracted by going outside in the cold weather.
Cold weather has nothing to do with getting sick. My mother used to tell me that going outside in the cold weather will cause the flu or getting a cold. But that's not true and is just an old wives tell.
Actually getting outside into some fresh air is better for your cold or flu instead of being cooped up indoors around all the germs.
I always get outside when I'm feeling good enough too when I have the flu or cold.