Place and weather influence people, no question about it; and to evoke both so that the reader will feel what characters experience strikes me as basic competence in a writer.
To the extent that our job is to cause the reader to have an experience, moreover, it doesn’t bother me if the setting is as much a character in a story as the people. Powerful renderings of nature or urban environments can be worth reading in and of themselves. The uneasiness aroused by the weirdly overlapping cities in China Miélville’s The City and the City has lingered with me long after I have forgotten the plot or details of the main character.
What’s important is to avoid meaningless cliché, which only brings a check box to the fore (midnight, moor, wind, dreary, check). To be art, the emotions and the place must be particular. Yet if you do it well, you can raise a reader’s heart rate even with a scene set on a windy moor at midnight (try reading Greer Gilman’s Moonwise if you don’t believe me).