Thanks for your question on Healthcare Magic.
I can understand your concern.
No, you should avoid running in
cold weather because this can worsen your
cough.
Possibility of viral upper
respiratory tract infection (URTI) related cough is more likely in your case.
So avoid cold weather for 1 week.
Do following things for better symptomatic relief and fast recovery.
1. Drink plenty of fluids orally and keep yourself hydrated.
2. Do warm water gargles 5-6 times a day.
3. Take levocetrizine 5 mg twice daily.
4. Avoid oily and spicy food. Avoid junk food.
Do all these for 1 week and you will be alright in 1 week.
Once you are fine you can resume running.
Hope I have solved your query. I will be happy to help you further. Wish you good health. Thanks.