To clarify some misconceptions here, indeed thyroid issues do show up often as loss of hair. As stated by yogi, indeed 'sometimes' the problem doesn't show, but that is due to the T4 test being run, not a complete T3, T4, free T4 being run. That would be preferable. However, if the skin is indeed purple, it's time for an abdominal ultrasound and a coagulation test to be run. Golden's are prone to certain illnesses that can cause internal hemorrage, and loss of hair is seen in many conditions of poor health. Also, seeing that this hair loss is bilateral, the adrenals should be checked on ultrasound and some endocrine testing should likely follow. If your vet is not equipped to run such diagnostics, as for a referral to an internist.
Good luck to you both.