Which is correct (or are both correct)?
They are walking on the snow.
They are walking in the snow.
If you are talking about going for a stroll, I would say in the snow. Unless you mean that the snow is so crunchy and hard that they are literally on top of it and not breaking through. Then they would be on the snow.
If you are talking about traction or comparing the surface when snow-covered to normal, then you would talk about how "walking on snow can be dangerous."