Grass is a slippery surface that will not anchor the snowpack unless it is mowed, like at some ski resorts. The same is true of deadfall timber, boulders and other terrain features. Dense trees will anchor the snow in place, but they must be so thick that they are annoying to travel through in order to provide adequate protection. They will not protect you from avalanches that start above the forest and run down into it, however. Vegetation, like bare rock, is relatively warm, so expect faceted crystal growth and hollow tree-wells.
Sparse trees can act as stress-risers in the snowpack.
They resist the downhill flow of the snow above them, creating tension. Avalanches frequently break across open slopes between trees or exposed rocks for these reasons. Vegetation can provide evidence of past avalanche activity, too. The type and age of the vegetation on a steep slope indicates the size and return interval for avalanches in a given path. Swaths through dense trees are an obvious sign of frequent large avalanches.