In the bowl of a stand add the whipping cream. Whisk on low-medium speed for 2-3 minutes, or until it's whipped and soft peaks have formed.
Add the sugar to a blender or food processor, pulse the sugar until a super fine (but not powdery) consistency is reached. Let the sugar 'dust' settle for a few seconds.
Add the sugar to a separate mixing bowl and stir in the wine until the sugar's dissolved.
Pour the sugared wine into the whipped cream and whisk just until incorporated.
Transfer the ice cream mixture to a rigid container, like a metal loaf pan or a plastic tupperware dish. Cover the dish and place it in the freezer until frozen firm, about 4 hours.
Scoop the ice cream into bowls and serve topped with the fresh berries. Splash with a bit more wine if desired.