Okay, let’s say that Mr. Burns decides to revive his old idea of blotting out the sun over Springfield, only this time, instead of getting shot by Maggie, he manages to pull it off. What happens to Springfield’s weather? Since there’s no sun, it’s going to get a lot cooler, but how cool? Will there always be snow in Springfield or will the temps be only slightly lower than areas nearby which get sunlight? More rain? Less rain?
I can’t believe I’m actually posting a serious reply to this post but…
IMHO, If the sun-blocker was about the same size and height as the sun-blocker depicted in the show, it would have no effect on Springfield’s weather. The town would never get as dark as it is shown in the episode, either. Even if it were much larger than it appears in the episode and able to articulate, moving across the sky and tilting to remain perpendicular to the angle of incident sunlight, Mr. Burns’ sun-blocker would be lucky to significantly darken a swath a few miles wide in the direct shadow of Mt. Springfield.
Outside this small area, refracted light would more than compensate for the shadowing effect, and advective heating from the surrounding areas would more than compensate for the lack of direct solar heating, even in the “shady” area.
There are plenty of places that are perpetually shielded from direct sun e.g. under overhangs or outcrops. If you want an area of a couple of square miles, many caverns meet the bill. If you want it to be in the ‘open air’, certain thick forest ang jungle canopies intercept all direct sunlight 80-100+ feet in the air. If that’s not 'open air enough for you, I’m sure you can find a sufficiently deep north-south crevasse. A week of heavy overcast would have far greater geographic extent than Springfield, but not the opacity you seek None of these approximate the Springfield scenario very well, but these examples do tend to suggest that there would not be a dramatic drop in temperature.
The gentlest of breezes could cross the occluded Springfield in under an hour, bringing a constant influx of outside heat, humidity etc. Any fairly modest wind could do so in minutes. You’d get a temperature gradient, but not much of one. If any appreciable gradient began to form, the heat-driven convection would just create more wind, and it wouldn’t take much wind to dissipate the gradient.