We don’t have ash berries here so I don’t know what they are.
The cage sounds like a good size. She will need out of cage time during the long winter.
Yes, you can hide things. Some people put treats in a paper towel roll. Insert treat and roll the ends shut. They have a ball tearing open the tube to find the treat. There are threads on the board that give ideas for overwintering squirrels. I will see if I can find a thread.
Cat trees and hanging ropes are nice. You can get very inexpensive cat trees on Amazon.