3 1/2 cups all-purpose flour (spooned and leveled), plus more for work surface
1/2 teaspoon fine salt
2 sticks unsalted butter, room temperature
2 cups sugar
2 large eggs
2 teaspoons pure vanilla extract
Green, red, and yellow food coloring
Whisk together flour and salt. In a large bowl, using a mixer, beat butter and sugar on medium-high until pale and fluffy, 4 minutes. Beat in eggs, one at a time, then vanilla. Reduce speed to low, add flour mixture, and beat until combined. Tint dough by mixing in food coloring: For trees, tint two-thirds the dough green; tint some of remaining dough red and some yellow; leave some plain. Divide green dough into 2 disks. Individually wrap all dough in plastic and refrigerate 1 hour (or up to 3 days).
On a large sheet of parchment paper, lightly flour both sides of 1 disk green dough, cover with more parchment, and roll out to about 1/8 inch thick. Repeat with second disk. Remove top sheets of parchment.
On a lightly floured work surface, roll pieces of red dough into thin snakes. Arrange on top of green dough in desired pattern. (If dough gets too soft to work with, refrigerate 10 minutes before continuing.)
Roll yellow and plain dough into pea-size balls and arrange on top of green dough in desired pattern.
Preheat oven to 350 degrees. Top dough with more parchment and gently roll over dough until decorative pieces are flush with green dough.
Carefully remove top sheets of parchment. With a 4-to-5-inch-tall tree-shaped cutter, cut dough. Transfer dough on parchment to baking sheets and freeze until firm, 15 minutes.
Remove cutouts from excess dough and transfer to newly lined baking sheets. Bake until set, 12 minutes. Let cool on sheets on wire racks.