Yes and no. As 'Vinny Valentine' says, going out in the cold for a long period of time weakens your immune system, making you more suceptable to virus.
Most people would find they get ill from sitting an air conditioned room, where the air is recyled, meaning you breathe in recycled air. You are at risk of illness here, especially if someone in the room with you is suffering from a cold, or flu.
The best treatment for a cold is to get on top of it the moment it comes. Strepsils, which you can get at your supermarket, cough mixture, Vicks Vaparub on your chest, and it's always good to invest in a Vapouriser.
These little machines are brilliant-fill them with water, put a special inhalant mixture in the lid, and switch on. The steam that is released helps to clear your airways, so you can breathe easier.
If that is too much infomation, I am sorry! 😉