Step 1: Make the brine: In a large saucepan over high heat, bring 1 quart of water and the salt to a boil. Stir with a wooden spoon until the salt dissolves. Stir in the ice water to cool the brine quickly. Add the drumsticks to the brine (make sure they’re completely submerged) and refrigerate for 24 hours.
Step 2: Remove the chicken from the brine and dry each drumstick with paper towels. Discard the brine.
Step 3: Set up the grill for indirect grilling and preheat to 375°F. Arrange the drumsticks in a single layer in the center of the grill, flattest side down. (The outside of the drumstick will have a more rounded shape.) Divide the wood chips between the piles of coals. Cover the grill and smoke-roast the drumsticks until the skin is crisp and nicely browned and the chicken is cooked through, 45 minutes to 1 hour. The internal temperature in the thickest part of the meat should be 180 to 185°F (higher than is recommended for chicken breasts).
Step 4: In the meantime, make the glaze: Melt the butter in a small saucepan over medium-low heat. Stir in the maple syrup and sriracha and continue to heat until the mixture bubbles, about 5 minutes. Set aside and keep warm.
Step 5: About 10 minutes before the chicken is done, brush each drumstick on all sides with the glaze and return to the grill. Repeat during the last few minutes. Arrange the drumsticks on a platter and drizzle with some of the glaze. Serve any remaining glaze on the side.