Toss together the sugar and lime zest. Run a lime wedge around the rim of the glasses, then dip and swirl into the sugar. Shake off excess.
Combine strawberries, rosé, Cointreau, honey, and 1/2 cup of ice in a high-speed blender and blitz until frosty. Add more wine if needed to thin. Divide into glasses and top with a fresh strawberry and mint leaves, as desired.