I'd wait until the end of February - you don't want to force new growth just yet. You can also put cuttings (5-6" long) into potting medium and maybe have extra plants grow. Good luck.

I think the desert willow would be better to wait until it is larger, unless you want to just do minor pruning of some small branches.

When you do want to prune, prune in the late fall, after the first frost has finished off the leaves for the season.

You can still prune before the first growth shows up, though.

I agree that the desert willow can wait for pruning, but I started pruning my vitex trees at a very young age. The vitex have been robust growers and want to grow more shrub-like than I want to have. I remove spent flowerheads after bloom and find they will repeat bloom if deadheaded. In February (when I prune my roses) I remove low branches and any new growth suckering from the ground or along the main trunks of the tree. I selected 3-5 trunks on each of the two trees, forming a nice multi-trunk small tree.
molly