I'll admit that +2 ev is probably too much to add. I went back and looked at old images I have taken, and it is more like +1 ev.
The Nikon matrix metering doesn't recognize snow. When the image is more or less uniform across the frame, it sets the exposure for 18% gray on average. This is about 1ev underexposed for snow.
Matrix recognizes when the top portion of an image is brighter than the bottom, which it interprets as sky over ground. Then, it increases the exposure to get the ground closer to correct while letting the sky blow out.
Your example images are slightly beyond the dynamic range of your camera.
In your last image, the dog looks good but the snow is still mostly gray.
There is no way in such a scene to expose both the dog and the snow correctly. In pp you can selectively boost the brightness of specific areas to make it look right. This is a form of HDR processing.