Hello Tommy2525,
Overwintering is a period when the plants go dormant. You prune back the bush/spent branches in preparation for winter and going dormant. The plant doesn't need to be watered while it's dormant since it's not growing. But the roots need to be protected from freezing temperatures (below 32 F) and drying out to much while it's dormant.
As I mentioned I would grow them in a
drip system so the roots are encased within a growing media like coco coir/chips, so they can be protected while their stored and overwintered. Also when the root systems get bigger they can be transplanted into larger containers each year without much root damage. Like from a 3 gallon bucket to 5-7 gallon buckets, and then to 10 gallon buckets.
I plan to grow raspberries, blackberries, and boysenberry's here in Arizona year round exactly that way in a greenhouse year round. Rotating the plants into a underground refrigerator to overwinter them so I can have year round production. There will be 3 sets of plants getting rotated every 4 months. Each set of plants will be rotated into the refrigerator where they will spend 4 months overwintering, then brought back into the greenhouse where they will spend the next 8 months growing.
One set of plants will be newly out of the refrigerator and starting to grow, the second set will be in full production with berry's to pick, while the third set will be in the refrigerator overwintering. At the end of the 4 months the set of plants that were in full production will be pruned back and rotated into the refrigerator for overwintering. At the same time the ones that have been in the refrigerator for the past 4 months will be brought out to start growing again. And the ones that were brought out 4 months earlier will be ready to start harvesting berry's from. This rotation will allow for a constant year round production of fresh berry's.