If he is feeding well, the weather would not interfere in his weight gain. From what you have described, it may be likely that there may be a problem with latching onto the breast and hence he is crying. Please consult a lactation consultant or your gynecologist or pediatrician for further support on this. As regards to the cough if it doesn't resolve with meds, I suggest u try nebulisation. That's could help resolve the cough quickly