Does the color of a heatsink affect its performance in dissipating heat?
I suspect it's unlikely, though it depends on what you mean by colour. There are three fundamental modes of heat transfer for any material, and only one of them is directly affected by colour.
Heat is transferred from the heat source to the heat sink, and from the heat sink to the air by conduction. Most heatsinks are made of copper (heavy, and relatively expensive) or aluminium - and copper is generally left natural, and aluminum either has a natural clear covering of Al2O3, or is anodised and coloured. For conduction, material rather than colour is important.
Convection is the movement of heat through the movement of air. While passive cooling simply uses this, you can increase its efficiency by increasing surface area (which is why heatsinks are finned), or by forced convection - blowing air to carry heat away. While air is not a good conductor, convection in air is how everything from cars to heatsinks are cooled. This is very efficient, and doesn't really rely on the material properties of the heatsink, or on the colour.
Radiation is... frankly awful at transferring heat unless you're in a vacuum (It also sucks in a vacuum, but conduction and convection cannot happen). It is affected by surface colour.
Practically speaking, a heatsink being coloured is entirely for looks, and will affect cooling less than surface area, airflow, material and the contact between the heat source and heat sink.
This Wikipedia article has some information/discussion about that. I only repeat some links below. For the complete discussion you can look at the article.
Heat Sink Color
How does the color of a heat sink impact its thermal performance?
In natural convection a black or dark colored heatsink will perform 3% to 8% better than an aluminum heatsink in its natural silverish color. This is due to the fact that dark colors radiate heat more efficiently.
In forced air applications, surface color does not increase a heat sink's performance due to the increase in convection. The color would provide cosmetic benefits only.
Does heatsink color affect heat dissipation?
Black is the best thermal body in terms of being a absorber or emitter. Let's assume a vacuum situation, if the surface "A" of a black heatsink is totally covered at T1 (temperature 1) by another black body at T2 (temperature 2), the black heatsink would get the energy reflected from another black body at reflection energy Ad(T14-T24) that we call "Stefan-Boltzmann" law of thermal radiation, here refers to Stefan Boltzmann Constant, it is 5.6697 x 10-8 W/m2?K4. Therefore if based on above, T1 is the temperature obtained from the black heatsink onto CPU, T2 is the ambient temperature around CPU. So if T14-T24 is a positive value, we know black is the best heat dissipation transistor since there is no thermal source around CPU inside PC case.
Do not paint a heat sink. Most heat sinks are anodized aluminum. Painting a heat sink (especially if it's a thick coat of paint) is like putting a blanket on the amplifier. If you absolutely must paint the heat sink, use the lightest, thinnest coat of paint possible.