OK what would happen if the Sun's temperature dropped a little, say 25% of what it currently is now? Would drastic changes happen here on Earth or the other planets?
Quite likely a massive ice age would ensue - and I don't know about you but, I'm heading to the tropics!
I'd imagine the tropics in this scenario would be warmer but not as warm as they currently are. It would be a lot more comfortable. Darwin is like 34 / 35 c all year round so it would become quite tolerable to live there than it is now.
Ignoring the fact that the sun's radius would likely have to stabilise at a smaller value, further reducing its luminosity (which goes as radius squared times the surface temperature to the power 4) the earth's effective temperature would also drop by 25% from 255 K to about 191 K so the earth would almost certainly freeze over. The decrease in the sun's radius would make things worse. A stellar photosheric temperature of just over 4000K corresponds to a K-class dwarf with a luminosity of about one-tenth that of our G-class sun. From the equation given in https://en.m.wikipedia.org/wiki/Planetary_equilibrium_temperature and assuming the albedo, emissivity and orbital radius of the earth are the same, the effective temperature of the earth scales as the stellar luminosity to the power 0.25 or 0.1^0.25 = 0.56. The effective temperature could drop as low as 143 K although that is still warmer than the boiling points of oxygen (90 K) and nitrogen (77 K) - the atmosphere would not freeze out although the carbon dioxide would (somewhere around 180 K approximately, according to the phase diagram, depending on atmospheric pressure, which scales in proportion to temperature) so its greenhouse effect would disappear. A snowball earth would also have a higher albedo, perhaps as high as 0.9 from its original 0.3, further reducing its temperature by up to a factor of 7, perhaps 50 K below the line where the mostly nitrogen and oxygen atmosphere probably becomes liquified - again not sure as the situation is complicated by lowered pressure and phase diagram considerations for the mixture of the two gases. Probably not easily survivable though...
As long as you're living around a black smoker on the bottom of the seafloor everything is great. Otherwise.. no. Of course there was enough warning time before the reduction in temperature happened, there could be massive projects to ameliorate the damage, but its still hard to imagine humanity surviving it, short of orbital habitats.
and we'd have to start breaking all of our rules very quickly to FORCE greenhouse gasses and global warming
TV personalities would run out in the mid-summer Florida blizzard in their heated environmental suits, and explain in detail how the suns temperature didn't really drop as frost and icicles forms on the camera lens and the wind continuously throws them under the rising snowdrifts.