For shrimp: Fill medium bowl with ice water; set aside. Combine 2 cups water, wine, and next 4 ingredients in medium saucepan. Bring to boil. Add shrimp; reduce heat to low, cover, and poach just until shells are pink and shrimp are opaque in center, 4 minutes. Using slotted spoon, transfer shrimp to bowl with ice water; reserve poaching liquid and lemon half. Drain and peel shrimp, leaving tails intact.
For dipping sauce: Squeeze juice from reserved lemon half into poaching liquid in pan. Boil liquid until reduced to generous 2 tablespoons, about 20 minutes. Strain; cool.
Mix crème fraîche, chopped chives, horseradish, lemon peel, and 1 tablespoon reduced poaching liquid in small bowl. Season sauce with coarse salt and black pepper.
DO AHEAD: Shrimp and sauce can be made 1 day ahead. Cover separately; chill.