If the engine will stay running when you give it more throttle then the idle speed may be set too low. Why? By giving the engine more gas when it is about to stall you are essentially compensating for too low and idle by increasing the throttle thus giving the engine enough fuel to stay running.
If the stalling at idle only occurs when the engine is cold then you may have a problem with the choke. Why? The choke restricts the amount of air going into the carburetor, thereby causing a richer air/fuel mixture that is needed when the engine is cold. If the choke is stuck in the open position then it will be creating a lean condition rather than the rich condition we need when an engine is cold and consequently stalling.
Another possibility is an obstruction in the fuel line or carburetor. Why? An obstruction in the fuel line or carburetor would restrict the fuel flow to the engine resulting in stalling.