A cold house cannot make you sick.
Although being in a cold house can lead to sickness because your immune system is not working properly and you could get pneumonia but the cold house is not the actual cause of the pneumonia.
Germs and viruses are what make you sick and the cold house can harbor more germs and viruses which can make you sick.
Your bodies immune system gets weaker when you're in a cold house or in a cold environment but the cold house itself does not cause sickness.
Also just like being out in the cold without a coat or clothes on at all cannot make you sick unless you came into contact with the virus or germs to make you sick.
Being in a cold house or a cold drafty house is not very comfortable though and makes your body work harder taking energy away from you.