That cloud cover is an important part of the climate I would say is self evident - a cloudy day in summer is likely to be colder than a day without clouds (the argument is not so clear cut when one also looks at clouds in winter, at least in higher latitudes, although near the equator clouds will always be associated with colder days).
Yes, magnetics are part if the issue - since solar activity is strongly linked to the magnetic flux of the Sun, and cosmic radiation reaching the Earth is also influenced by the Earth's magnetic field.
I wonder exactly how much influence clouds actually have, they are not opaque to the entire spectrum of radiation, and at night they work in reverse, they block outward infrared.
Think our magnetosphere plays a pretty large part in blocking cosmic radiation. (Always wondered how much that would deteriorate during a pole-reversal,but probably don't really want to know, at least not find out the hard way.)