Place ricotta in a fine sieve set over a bowl; cover with plastic wrap. Refrigerate until drained, at least 2 hours or overnight.
Break off a portion of the top of each cone to create a 1 1/2-inch-deep arc on 1 side. Holding each cone at an angle, dip about 1/4 inch of rim into melted chocolate, and immediately sprinkle with pistachios, reserving some for garnish. Transfer to a parchment-lined sheet, broken side up. Refrigerate until set, about 10 minutes.
Mix together ricotta, sugar, wine, and vanilla seeds. Mix in orange peel and chocolate chips.
Transfer ricotta filling to a pastry bag fitted with a large open-star tip. Pipe filling into cones. Sprinkle with reserved pistachios. Serve immediately.