Agnostic, look at figure 1 from the paper. There is nothing there to infer anything quantitatively about NH total snow cover, which is what Willis analyzed. Most notably, our analysis clearly says nothing about any change in large regions of Russia and Canada. The moisture source from the open water in the arctic ocean is secondary to the atmospheric circulation change.
In the conclusion, the words used are “The results of this study add to an increasing body of evidence . . .” are the appropriate words in my opinion. The “we conclude” statement in the abstract (where word numbers are limited) comes across a bit strong, but I think the more thorough statements in the the Discussion are appropriate. Again, some of these words are not mine such as “load the dice”.
IMO the significance of this paper is in understanding seasonal snowfall variability, which is a goal of seasonal forecasting.