Hi there!
This does sound like frost-bite, and the black part of the tail is probably dead tissue. It may not cause a problem, but keep an eye on it for now. The rat might start gnawing at it as she does not feel the pain, and rats like to chew on things, and this might cause infection. If it spreads so the black area gets bigger, or if it seems to cause her any discomfort, you should take her to the vet and remove the tip. This should be a relative straight forward procedure, however, general anaesthetic in small furries can be risky. So keep an eye on it for now.
Hope this helps, let me know if you have any further questions!
Dr Beurling
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