From NASA's Solar and Heliospheric Observatory's "Not So Frequently Asked Questions" section: Q-Does the number of sunspots have any effect on the climate here on Earth?
A-Sunspots are slightly cooler areas on the surface of the Sun, due to the intense magnetic fields, so they radiate a little less energy than the surroundings. However, there are usually nearby areas associated with the sunspots that are a little hotter (called falculae), and they more than compensate. The result is that there is a little bit more radiation coming from the Sun when it has more sunspots, but the effect is so small that it has very little impact on the weather and climate on Earth.
However, there are more important indirect effects: sunspots are associated with what we call "active regions", with large magnetic structures containing very hot material (being held in place by the magnetism). This causes more ultraviolet (or UV) radiation (the rays that give you a suntan or sunburn), and extreme ultraviolet radiation (EUV). These types of radiation have an impact on the chemistry of the upper atmosphere (e.g. producing ozone). Since some of these products act as greenhouse gases, the number of sunspots (through association with active regions) may influence the climate in this way.
Many active regions produce giant outflows of material that are called Coronal Mass Ejections. These ejections drag with them some of the more intense magnetic fields that are found in the active regions. The magnetic fields act as a shield for high-energy particles coming from various sources in our galaxy (outside the solar system). These "cosmic rays" (CRs) cause ionization of molecules in the atmosphere, and thereby can cause clouds to form (because the ionized molecules or dust particle can act as "seeds" for drop formation).
If clouds are formed very high in the atmosphere, the net result is a heating of the Earth - it acts as a "blanket" that keeps warmth in.
If clouds are formed lower down in the atmosphere, they reflect sunlight better than they keep heat inside, so the net result is cooling.
Which processes are dominant is still a matter of research.
http://sohowww.nascom.nasa.gov/classroom/notsofaq.html#SUNSPOT_CLIMATE
