That very question can be answered many different ways; should it include snow? should it have a certain color cast to it? does it need to show friends & family around the table in celebration? should it show warmth somehow? should it be at a certain time of day or night? All these questions can be answered either yes or no, depending on what your vision of winter is and how you wish to portray it. I’ll pick mine apart for the sake of providing an example.
My vision of winter usually does include snow because it shows the time of year & weather that i’m comfortable with, even though it may not snow often where I’m from. For me, the issue of it having a certain color cast depends on the lighting, not necessarily on my vision, even thought it should be reflective of that vision. It doesn’t need to have family or friends, mostly because I’m not much of a people photographer and I’d rather stick to what I’m comfortable with in that department. Snow doesn’t usually entail warmth, but including some kind of it to the shot provides it with a good temperature-themed contrast. As for it being at a certain time of day, it doesn’t matter much to me, as long as it somehow has a sense of feeling to it; sunrise or sunset on snow or frost does make for some pretty good photographs though.
There are many different ways to answer the question, but the beauty of it is that we actually get out and make the shot. I say this because it’s all in the action of making, taking & refining it, that provides the best experience photography has to offer. Just reading about it doesn’t have the same level of fulfillment because there is no actual, physical movement involved. The best part is the actual movement & learning as you do so because it helps you stay active and somewhat aware of what is happening around you.