I also wanted to make something festive and wintry without being obnoxiously red and green. I love the look of the dark, bare tree branches poking out of the snow in winter.
I found it easier to cut the longer strips ahead of time and sew them with a zigzag stitch, using the same color thread as my branch. Make sure to reverse stitch at either end of the branch segment so the thread doesn't loosen later on.
The smaller branches were easier to sew first and then cut. I sewed a rough line down the doubled fabric for each - I didn't want them to be perfectly straight or they wouldn't look as natural to me. I made some of them branch by sewing a connecting zigzag stitch heading off in a slightly different direction. I cut the small branch segments one at a time after each new line of stitches was sewn.
Once I had all the branch segments, I sewed the large pieces together, making sure to leave a little overhang so that the tapered end could branch away from the main strand. I wanted this to feel a little less 2D, so I opened up the fabric at the sides of the branch strips (since they were sewn down the middle), pressing them open so that my fingertips were pressing the seam, and sewed them together along that opened seam.