We study the consequences of the formation of dust in cold clouds deposited in cooling flows. Such clouds are inferred from absorption seen in X-ray spectra. Although the gas is initially above 10(7) K and presumably devoid of dust, we postulate that dust forms in the cold, dense, molecular cores of cooled clouds. If the dust spreads through the cloud, it causes all but an outer column density of 10(20) cm(-2) or less of the cloud to be highly molecular and cold (approaching the temperature of the microwave background). Much of the molecular gas may then freeze out on to the grains. Such dusty cold clouds can then escape detection by current observations aimed at HI or CO. Either in the very core of the flow where cloud-cloud interactions occur or where a radio source disturbs the clouds, dusty emission-line and reflection nebulae will be found. Such disturbed regions are relevant to observations of the emission-line nebulae and excess blue light in cooling flows, the optical alignment effect in distant radio galaxies and the formation of dust lanes in elliptical galaxies.