Since DuckHunt V4.1, when buying a coat in the shop you'll be given a randomly colored coat. Additionally, with prestige level 2 or more, you are even able to select a specific color yourself (
dh!shop coat <color>).
Every color will give you a small, different power up.
A useful coat when it rains
Better visibility: Increase your chance to frighten ducks, and reduce your chance to get shot by another hunter.
Lower visibility: Less chance to frighten ducks.
Lucky find: Increase your chance to find items in bushes.
Hungry for blood: Increase your murder skills, reduce murder penalties.
Sun powers: Mirrors are less effective against you.
Farming skills: Clovers give you one more experience point.
Secret service: Sabotages are cheaper.
Sea powers: You are immune to water buckets.
(As do all the other coats, so this one is indeed useless)
Power of love: You can't kill players with the same coat color.