Both of those questions were asked, and answered, unofficially:
Does Dispel Magic work on Tiny Hut? -Yes, as long as the hut itself is in range.
How does the Control Weather spell interact with the Dispel Magic spell? -Yes, because you're probably inside it already so you're in range. BUT you have to figure out that weather is magical first, because "detect magic" works on
objects, and environmental effects are not physical objects. Plus even if the spell is stopped, the current weather will just keeps going until it dies down. - You just stop the external magical influences, but not what is already going on. So it ain't gonna help you much in the middle of a blizzard.
And yes, Dispel Magic has always been stupidly OP regardless of editions. (It's actually weaker in 5E; Like in 4E you could literally end the weather right there.)