White is Black, Black is White, Night is Day
People sometimes say that two things are like "night and day" to mean that they are at opposite poles, as far apart as possible. Black and white are supposed to be where they're supposed to be. But actually, the choice is all yours.
Most photographers set their camera on auto-exposure, perhaps not really even fully understanding how to determine correct exposure on their own. No real problem there since cameras today generally seem pretty good at exposure. But what is "correct exposure" anyway? Basically, an image is correctly exposed when it comes out exposed the way you wanted it to. When you think about it, your camera may auto-expose most images the way you would have wanted it to, but the best way to achieve this is if you learn to set exposure for yourself.
I'm not going to discuss how to get the exposure you want. I've written about that before. Instead, I want to focus on the subjective nature of "correct" exposure. It really is up to you. You can expose an image to be as dark or as light as you want. Really.
Imagine a scene, any scene. What does it look like when you close your eyes or turn out the lights? Pretty dark, right? That's what happens when no light gets to do its job. Of course the exact same thing happens with your camera. Images will come out pretty dark if not enough light gets through, whether that be from a small aperture opening, a fast shutter speed, a low ISO setting, or a combination of the above.
This likely doesn't come as a surprise I'm guessing, but the extremes that this makes possible often do surprise. Or even when this isn't the case, photographers generally limit their creative exposure adjustment to minor tweaks, often only those needed to mitigate technical issues such as movement from blowing wind or exposure issues elsewhere in the frame. Rather than dealing with motion blur from the wind, it can make sense to compromise by slightly underexposing so that the shutter doesn't have to be held open any longer than necessary. Rather than living with a burned out sky, a photographer may choose to slightly underexpose, thereby rendering then foreground a tad darker than normal.
The truth though is that you can make just about anything come out exposed any way you want. Even solid white subjects will be rendered as black so long as little or no light reflected off it reaches the camera sensor while the shutter is open. Imagine a photograph shot in a completely dark room or on a moonless night. White becomes black.
But the reverse is also true. Take that white object on a moonless night and leave the shutter open long enough and you will get a white subject to show up after all. But more surprising, were that subject itself black, you can still expose it sufficiently to make even that look white. Black becomes white. So long as even a small amount of light is present, it will eventually build up to create an exposure that renders as white.
It's all up to you. Your camera will likely never do this on auto-exposure. Indeed, it sees everything as neutral gray. You get to see things any way you want to. Not only can you over expose snow slightly to make it show up white instead of gray, you can choose the mood by selecting just how bright you render it. You can turn an otherwise ordinary scene into an iconic silhouette by sufficiently underexposing, provided as well the background is lighter than that subject to provide contrast. You don't need to always strive for images that look the same as your eye sees them. Your eyes automatically adjust exposure just as most modern cameras do by default. But that doesn't make things wrong if images come out lighter or darker than that. It just means you're rending them in a different light. Just like other creative aspects of photography, exposure should be interpreted simply as "average" or "ordinary." Reaching for a wide angle lens or telephoto for creative reasons makes perfect sense. So too should reaching for a non-default exposure.
You can over or under expose intentionally if you so choose. You can make day into night, or night into day. There is no such thing as "correct exposure" apart from whether or not an image comes out exposed the way you want.
The possibility of over and under exposure isn't a bug, it's a feature.