Does being cold make you sick?

My friend was snoring very loud so I turned on a fan to drown out the noise. I already gave her all my blankets and my comforter and it is not even cold in my house. She started complaining about how she’s gonna get sick from the air and to turn it off . But I didn’t so she went to go sleep in the living room. Was that mean of me to do? I have heard it is a myth you get sick from being cold and the fan is not that cold. What do you guys think?