Booking hotels in the Swiss Alps during ski season... Difficult.

We're finally making some progress on the plans for our March Switzerland trip. Although, it should be noted that finding and booking hotels in the Swiss Alps during the ski season is far from being easy.
We've decided to split our time between the "High Country" and the "Low Country." Or, in non-Swiss, we'll spend four nights in a small town in the Alps and three nights in the valley city of Lucerne.
We'll make day trips from each of these locations which, from what I've been reading in numerous Switzerland travel books I collected from the library, should be easy given the excellent train and transportation systems in place in the country.
We've really narrowed our hotels down to two at this point: