I might have Raynaud's, could I do an experiment on myself and put my hand in ice water for different durations of time and see how long it takes for my hand to reach normal body temp (~37 deg C)?
Raynauds is a lack of blood supply to the extremities. Putting your hand in cold ice water is a bad idea. The appearance of pallor and pain in your extremities itself is a sign. It is not life threatening and can be cured.