A.A.
I wouldn't take him out in the cold, would you want to be bundled up and taken outside if you weren't feeling well? I understand the cabin fever, but don't think it's worth it. Cold air and chest congestion isn't a good combination, it'd most likely make him cough even more. As for the nursing, as long as he is having wet diapers as frequently as normal and is not showing any signs of dehydration, don't worry too much. Offer it frequently, pump if you need to, and let the little guy get some rest. Does he drink from a sippy? You can give him breastmilk or water in it to keep him hydrated. Laying down to nurse might make him uncomfortable, sitting up with a cup might be a good way to get some fluids/calories in him. Good luck, hope he is feeling better soon!