The ABS module is basically what controls the Stabilitrak. If there was an issue with a wheel size mismatch, the ABS light would also come on.
If only the Stabilitrak light comes on, then it's likely the steering wheel position sensor, which is the only part that is exclusive to the Stabilitrak system. All the other parts are shared with the ABS system. If there was an issue with any other part, both the ABS and Stabilitrak lights would be on. The SWPS is a common failure part and is known to do this intermittently like yours is doing, especially when cold. To turn off the light while driving, turn the key momentarily to START. If the light comes on just as soon as you turn the steering wheel, it's the SWPS.