Probably one of the more enduring lines in literature has to do with the weather. "It was a dark and stormy night" was, I think, an actual line from a book. Whether it preceded Snoopy typing on his dog house or not I'm not sure, though it could well be argued that without Snoopy the line would have passed largely into obscurity. It has its problems as a written line, not least of which is a clear violation of "show don't tell." (Though that particular rule has struck me as at once over-simplistic and a too oft used club to bludgeon works with which we do not agree... but that's for another day.)
Despite it flaws, it has a simple appeal that sticks with you, and if nothing else it calls up a specific imagery. With apologies to Charles Schultz, if you take Snoopy out of it and just approach it on it's own, it sets an ominous scene. I myself picture lashing rain, flashing lightning, and crashing thunder. Spooky old home or half empty but equally old and spooky old hotel optional, but it works for me. It would also work well for some character out and exposed to the elements, though somehow for me that only seems to work if it's in an open field with tall grass to blowing in waves before the wind.
My point in all this is that, with a line like that, the weather becomes central to the narrative that follows. It's impossible to ignore the weather once you've opened with something like that, and that can be good or bad. I tend to feel the weather plays a vital role in setting the scene, especially if it is stormy or wintry or too hot. ("To build a fire" could be argued as being entirely about the weather and the protagonist's struggle against it.) I also feel it only ought to be mentioned specifically if it's integral to a scene. Otherwise the overall time and setting can do it for you. If it's winter in Duluth you would hope readers will catch on that it's cold and snowy, as opposed to summer in New Orleans.
It isn't always necessary to talk about the weather, and sometimes it's just extra details that bog down the scene. Sometimes it's just cliche, too, because it seems somehow in every Bronte or Bronte-esque story I've ever seen or read, at some point the heroine must battle the elements in some sort of scene that the literary types laud as standing in for her struggles with life or love or some other highbrow hogwash. (Those same literary types tend to then denigrate when pop/pulp authors do the same - as though somehow the rules change. Again, another post.)
And when you do, you also have to bear in mind everything that goes with it. Just because I've grown up with snow and cold and ice in the winter all my life, and so I know what all that entails... but if I achieve even any small amount of success, my works may be read by people who've never experienced. And who may not know that, when the temperature drops into single digits, your hero had better cover his nose if he wants to keep it when he goes outside for any length of time.