Weather and season are important components for setting the scene for a reader as well as inferring the physical and emotional states of the characters. However, it is difficult to write within a season without falling into cliche. There is just so much description of slate gray skies or fields of dipping violet wildflowers that can be written before it becomes cliche and predictable.
Originality really takes some work, though I also suggest not trying to reinvent the wheel (i.e. it is cold then say it is cold because sometimes straight forward is the way to go).
One of the best ways to set the context as you write and the proper mood is through music. That's why there is so much music on this blog. All of art is compliments all artistic creation.
The best music I've found for setting tone and ambiance for writing about winter is Schubert's Winterreise song cycle sung by Dietrich Fischer-Dieskau. If you have Spotify, I highly recommend a subscription, then there are a number of good recordings for you to listen to.
Below is Gute Nacht, which has about as wintery a feel as you will find anywhere, and Der Leiermann. This may not be your cup of tea for just listening to music, but it will help set a stark winter mood.