You could add a dash of red or orange in the form of a few bunches of berries and that would highlight nicely but for sure you don't want to go overboard. You could do natural colour antlers too and get that dash of beige.
Pyracantha berries still attached to the branches. That'll keep hands out of the arrangement too. Holly berries tend to be associated with Christmas. Some white beautyberry bunches would look neat too.
Yes you want it to be distinguished from a Christmas arrangement. These would be great!
Looks nice. I feel like it could use a single color in there somewhere, but anything you add would probably ruin it.