This is not true in a fan situation and I wish folks would discontinue posting it. The truth is the opposite - chins need constant ventilation, especially when you have multiple chins. The more air movement the healthier your herd.
A draft is not a fan blowing. I've got five in a 12 x 12 room and that place is like a wind vortex.
It is common animal husbandry 101 that you do not enclose areas where animals urinate due to ammonia. This includes the little box we call a house!
) Fortunately most people come and go enough that the doors of the house vent it and the a/c and heater circulate the air constantly. All modern houses with central units are required to have a small fan running that circulates air - as well as modern cars - for circulation/suffocation reasons.