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Clouds are basically made up of tiny water droplets. When minute particles in the atmosphere become ionized by incoming GCRs they become very 'attractive' to water molecules, in a purely chemical sense of the word. The process by which the Sun's increased magnetic field deflects incoming cosmic rays is very similar to the way magnetic fields steer electrons in a cathode ray tube (old-time television tube) or electrons and other charged particles around the ring of a subatomic particle accelerator.-etl

So....fewer sunspots = more GCRs reaching earth, resulting in more low-level moisture-laden clouds.

Does this equal more precipitation, despite the cooler weather ?

One of the requirements for an Ice Age, or so I used to read, was increased precipitation to convey moisture to higher elevations where it dropped as snow, resulting in glaciers, which formed as the earth was cooler, and snow at higher elevations did not melt during the summer.

Have I got this right ?

When the Little Ice Age hit in the early 1300’s, the stable summer weather disappeared and one the most recorded weather phenomenon was spring and summer rain...lots of it. It made the fields too muddy to plant, and it beat down the heads of the grain that did grow into the mud where it couldn’t finish maturing and rotted.

There was a lot of famine very soon after the change occured. It took Europeans a surprisingly long time to adjust to the changed weather, with the Dutch first and the English second diversifying their crops and rotating their crops and doing drainage techiques to recover land made soggy and enclosing land for pasture and raising more animal stock (which also manured the pasture that was later rotated back to crops). They piggy-backed a crop after they harvested what grain grew, generally turnips for feeding their animals during the winter as the traditional fodder crops failed.

Doing these things, the English actually went into a food exporting nation for a while. The French resisted change and hence their revolution, when there was no grain to make the traditional staple of bread.

Source: The Little Ice Age, by Brian Fagan