Why dont you get chill bumps on your face?
The chill bumps are caused but a small muscle attached to a skin-hair, which is serves as a heater when activated. Face does not need skin-hair muscle heating, it has enough blood circulation and lots of under-skin facial muscles.
I get chill bumps on my face and the rest of my body as well. They are not derived from being cold but from emotion. So it is possible as it happens to me on a daily basis.