I think you have your zone system rules confused.
If you are exposing for shadows with details, and developing for highlights, where does over exposing and over developing come in when contraction is what's need here?
With properly tested development, you are under rating your 400 ASA film for the developer/film combo not as compensation for exposure. If for example, using Microdol-X with TMY, you tend to loose a stop because this developer has a low activity level, thus the need to rate the film at 200 to print 9 zones on a number 2 grade paper. It has nothing to do with exposure but more about the activity of the developer used in combination with the emulsion to render a "Normal" print. If using HC110, on the otherhand, there is no loss of ASA rating in this combination since the activity level of this developer is much higher than Microdol-X, which will tend to block the highs faster, making the film rating faster in this developer.
After rating your film/developer, expose for shadows with details then place that reading in in Zone 3 to render a rich black with detail. Read the white highlight of the snow and you'll see it will be well above 7 stops difference. This situation requires under development in order to keep the highs form blocking up since the shadows have fully developed in the first half of the development process but will continue to develope the highs to an unprintable desity. This scene needs contraction not expansion in order to be able to print 9 zones and yet maintain details in both shadow and highlights. So underdeveloment will not effect the shadows but will underdevelope the highlights forcing them to fall in a printable range of the #2 paper.