Very pretty cake. I think modeling chocolate would be easy, but you coud use fondant, too. Use the image you have for placement of the branches.
I agree with Lapazlady. Modeling chocolate would be the easiest option because you would already have the desired color and it would stick right onto the cake. I just started working with modeling chocolate and I love it.
Whenever I have to make branches like these-I have success with fresh tootsie rolls-candy rolls out into any size branch you need and will stick to icing before it crust.
If icing has crusted-brush branches with clear vanilla using a brush-dampened not dripping wet-to attach branches.
Happy Baking and Decorating,