Whisk together flour and salt. In large bowl, using 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 paper, lightly flour both sides of 1 disk of green dough, cover with parchment, and roll out to 1/8 inch thick. Repeat with second disk. Remove top sheets of parchment.
On lightly floured surface, roll pieces of red dough into thin snakes. Arrange on top of green dough in desired pattern.
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 4-5inch 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.