What is the relationship between colour of a material and its emissivity?

White colored materials absorb less radiation that black colored materials. Hence two materials that differ in color only - regardless of the material type - will have different emissivities.

If we're talking about clothing, then it's as you said, white reflects all visible, some uv, and some IR. On the contrary, black absorbs nearly all wavelengths of light in the uv-vis-IR region. Therefore if one was to wear an arbitrary black cloth, it absorbs radiation, and then by conduction this 'heat' is passed to your skin via air and moisture, in comparison to white cloth which will keep you cooler because there is less energy/heat which can be transferred to your skin. Obviously this neglects the potential difference in cloth thickness and/or weave between different cloths, which is why some people even in hot countries wear black.

Practical examples based on differences in light absorption of surfaces can be observed at oil refineries. In fact, white coated tanks usually contains volatiles products, such as gasoline, in order to get them refractories to sunlight avoiding excessive evaporation. On the contrary, those black painted are for the heavier oil fractions and crude oils, to increase sun radiation absorption and thus lowering their viscosity. Also, the so called ¨desert clothing¨ is white to decrease the effect of sunshine heat.

Remember that the visible light is only a part of the electromagnetic spectrum. So when you speak of emissivity, you should rather speak of spectral emissivity which means emissivity at a certain wavelength. What Martin and Machado say is true but only for the visible light which has the highest energy in the electromagnetic spectrum (see Planck's law). But, e.g., if you consider the infrared radiation between 8 and 12 microns, we measured that a white dull paint has a sligthly higher emissivity than a black dull one.