Baby with a cold and air conditioning

My baby is 4months +11 days old. She has gotten a cold. She had one when it was still hot out so we continued to use the air conditioning. My apartment gets very dry with no ac on and I can't open the windows because the Temps drop during the night and gets too cold. My question is will the air conditioner make baby more sick? I dress her in a fleece pj with a short sleeve onsie under. The house temp stays at 73/74. I know heat will make her more stuffy. I do have a cool mist humidifier but she still seems to get stuffed up. Any suggestions please???