Chemical models predict that in cold cores gas-phase methanol is expected to be abundant at the outer edge of the CO depletion zone, where CO is actively adsorbed. CO adsorption correlates with volume density in cold cores, and, in nearby molecular clouds, catastrophic CO freeze-out happens at volume densities above 10(4) cm(-3). The methanol production rate is maximized there and its freeze-out rate does not overcome its production rate, while the molecules are shielded from UV destruction by gas and dust. Thus, in cold cores, methanol abundance should generally correlate with visual extinction, which depends on both volume and column density. In this work, we test the most basic model prediction that maximum methanol abundance is associat...