My first version of this corrects the sky and the blue cast on the snow, by almost eliminating the saturation in the Orange, Yellow, and Blue channels. I have then brightened the snow by increasing the luminance of the blue channel. Overall I have also reduced the vibrance of the image and corrected the exposure to set a white and black point.
As an alternate to this interpretation I also went with a much softer show, reducing the exposure and the Blacks, but most significantly shifting the Clarity slider to the left which dramatically reduces the sharpness of the image, softening the view:
In both of these case the images have almost become monochrome, the red of the persons jacket in the foreground and some street lights in the trees being the primary source of colour. The sky is still a little red, I cannot easily remove this without reducing the colour of the lights in the trees. At rpesent I am managing these images using the overall development tools in Lightroom, clearly using masks I could selectively change areas of the screen. However, I think that is stepping from adjustment to modification, not the point of this exercise.
As mentioned these two images are virtually monochrome, so I have stepped them fully to black and white:
In the first image I have increased the contrast further, whilst in the second I have dropped the clarity as far as possible creating a very misty look. The first photo creates an impression of stark cold, whilst the second is a misty grey day.
I have also tried to work with the sky to make it warmer, perhaps even suggestive of evening rather than morning, however, the colour cast is too strong and all I can achieve is a very moody alien look:
In this case I have adjusted the red and orange hue to push the sky towards red, whilst desaturating the blue/purple channel to keep the snow white. What this demonstrates is how easy it is to get this process wrong and create very strange effects.
My final interpretation is a crime against photography, but a bit of fun to do. It seems very popular today to create an antique look in black and white images, adding sepia, grain, and vignetting to replicate and aged photograph. Here is my go:
I now have to go outside and shoot myself.