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More seriously, aurora is associated with cold weather, but that's because it's generally much colder during clear nights.
I guess that would be visibility of the aurora, since the aurora is still present even if it is cloudy. As for climate, the link is fairly well understood, with lower sunspot number related to decreased solar irradiance which cools the planet. There are some complicating factors that appear over longer timescales though, such as how it modifies the formation of clouds. But in geologic history these do not appear to be very important, and the majority of climate history is well understood without invoking changes in the Sun. (Unless you go to very long timescales -- millions to billions of years -- over which the Sun's luminosity has been increasing, but the rock-weathering cycle acts as a natural thermostat to balance it.)
The Little Ice Age is interesting. It was caused by a combination of lower solar insolation and a period of volcanic eruptions
, both of which are negative forcings (prolonged low sunspot activity correlates with decreased flux, and volcanic eruptions produce sulfur aerosols that block sunlight). So in a sense the last few centuries of warming has been in part a recovery from the LIA, but humans are adding an additional greenhouse forcing on top of that. The magnitude of that greenhouse forcing is a lot larger, especially going into the 21st century.
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And if the warming seriously fails to follow climate models, don't be surprised if you hear people on the other side suggest that the expected warming has been masked by low solar activity. Attribution is a messy business.
Solar activity is measurable, so if that happens they must show that it is consistent with the observed change in forcings. Historically, high vs. low solar activity can modify climate by a few tenths of a degree. But the magnitude of projected warming (what CO2 concentration curve we choose to follow) matters more by about an order of magnitude. If greenhouse gas concentrations go up a lot and the temperature doesn't, then it won't be possible to blame the Sun unless the Sun does something very observably crazy.
More likely people will point to internal climate variability (especially, what was the ocean doing?), but even then they must show it is consistent with observations of what those systems have been doing. Several degrees of temperature, globally averaged over the surface, is a lot of energy, and it is hard to hide that much energy without leaving clues.