Are there any opening traps where your opponent can blunder into a windmill?
I did some deep, deep searching and found few results. It seems that there is no actual windill traps that are quick and widely know, unless you somehow manage to run through long and arbirtary seuqences that are extremely unlikely to occur in actual play, and even then it is a matter of your opponent actually falls for it.
If you still consider it a trap though, the one genuine such trap that I have discoverd so far occurs in the Russian Game, Damiano Variation.
[FEN ""] [startply "26"] 1. e4 e5 2. Nf3 Nf6 3. Nxe5 Nxe4 4. Qe2 Qe7 5. Qxe4 d6 6. d4 dxe5 7. Qxe5 Qxe5+ 8. dxe5 Nc6 9. Bb5 Bd7 10. Bxc6 Bxc6 11. O-O O-O-O 12. Bf4 g5 13. Bxg5 Rg8 14. Bxd8 Rxg2+ 15. Kh1 Rxf2+ 16. Kg1 Rg2+ 17. Kh1 Rg3+ 18. Rf3 Bxf3#
The trap occurs when Black plays 13... g8. If White striks the false prey with the move 14. Bxd8?, thinking they have won an exchnage, then Black can play 14... Rxg2+!! and commence a mate in 4 using the windmill tactic.
Another alternative, as user @supercat suggested in a comment, is that black could decide to be a bit of a troll and have fun demonstrating the power of the windmill.
[FEN "2kB1b2/ppp2p1p/2b5/4P3/8/8/PPP2PrP/RN3R1K b - - 0 1"] 1... Rxf2+ 2. Kg1 Rg2+ 3. Kh1 Rxc2+ 4. Kg1 Rg2+ 5. Kh1 Rxb2+ 6. Kg1 Rg2+ 7. Kh1 Rxa2+ 8. Rf3 Bxf3+ 9. Kg1 Bc5+ 10. Kf1 Rxh2 11. Ke1 Be3 12. Nd2 Bxd2+ 13. Kf1 Be3 14. Ke1 Rh1#