Is it possible for cold air intake to be on a carb?

 

Yes, the old Monte Carlo SS for instance has a hose to the front that I would define as a cold air intake. But it also has a thermostatic controlled flap that feeds a constant room temperature air to the carb. This is quite common. The hot air can be blocked off (unless driving in sub-zero temps).

 

The stock air cleaner set-up does exactly that.