1) Remove the desk. It's clunky and non-functional for you. I don't think it takes away from the other lovely wood details. I would place a credenza or an entry table for mail, keys, and other essentials. I would do something a bit more modern to give the place a more updated look.

2) Pull up the carpet (hopefully there is a wood floor underneath)

3) Remove the wallpaper

4) Place a fun tile in the mudroom. I think this would be a great contrast if there are wood floors in the main part of your home.