I've had frost bite a couple of times. More than color change, I remember the stinging pain and the complete lack of feeling in the toes that were affected. Most of the time, I wasn't in a situation where I could look at the color. Did you have the stinging pain?
I found some color descriptions that may help (below). If the tissue is damaged, then you really shouldn't expose it more. I'm concerned about the spots you say are forming. They are not mentioned, however, in the notes below.
Skin also changes color when exposed to extreme cold. It blanches, then may appear red, and finally white-purple if allowed to freeze
Second degree, superficial frostbite: The skin will be white or blue and will feel hard and frozen.
Third degree, deep frostbite: The skin is white, blotchy and/or blue. The tissue underneath is hard and cold to the touch