A cold is caused by a virus and you need to catch it from someone else who has a cold. So if the window was open and someone with a cold walked past sneezing or coughing then possibly. The only effect otherwise is that by sleeping under the window, it created the right conditions for a cold he had already caught to develop. If you do sleep with a window open and it is cold, you can have the symptoms of catching a cold (blocked nose, dry throat, thickly cough etc.), but this will soon pass once you have warmed up and had hot food and drink as they are only the bodies natural reaction to being cold.
