Preheat the oven to 350°F. Line a baking sheet with parchment paper.
In a mixing bowl, cream the softened butter with 1/4 cup of the powdered sugar until smooth. The butter should look pale and fluffy, not shiny or soupy. If it looks greasy or has started to melt, pop the bowl in the fridge for 10 minutes before moving on, since melted butter is the main reason these cookies spread instead of holding their round shape.
Stir in the flour, oats, coconut, walnuts, and salt until just combined.
Gently fold in the chopped cherries with a spatula, just until they are distributed through the dough. Overmixing at this stage crushes the cherries and turns the whole batch pink. The cookies will still taste great, but if you want to see distinct red flecks instead of an all-over blush, stop folding as soon as the cherries disappear into the dough.
The dough should hold together when you press a spoonful between your fingers, somewhat crumbly like a shortbread dough but not falling apart. If it feels dry and will not come together, work in softened butter one teaspoon at a time. If it feels sticky from the cherry juice, chill it for 10 to 15 minutes before rolling.
Roll the dough into 1-inch balls and place them 2 inches apart on the baking sheet. Do not flatten them. Bake for 12 to 14 minutes, until the bottoms just start to turn golden. Pull them before the tops brown, since a few extra minutes in the oven is what turns these from tender to sandy and dry.
Let the cookies cool for 2 to 3 minutes on the sheet, just until you can handle them without burning your fingers, then roll them in the remaining powdered sugar while they are still slightly warm. The warmth is what makes the sugar stick in a thick, even coat instead of sliding off.
Once the cookies have cooled completely, roll them in powdered sugar a second time for that fully snow-covered look.