A great thought experiment for the doubters goes as follows:
You are flying an aircraft in level flight at 60 knots in a 30 knot headwind.
You decide to fly an orbit, still in level flight, at 60 knots, at 30 degrees angle of bank.
You put in the 30 degrees angle of bank, and increase power to maintain your 60 knots. You also increase your pitch attitude to maintain your altitude.
During the complete orbit, will you have to change your power or pitch attitude due to the wind?