There are a few cases in history of people falling into severe hypothermia and then recovering. The scenario closest to what you want that I can remember is that of Anna Bågenholm.
Anna Elisabeth Johansson Bågenholm (born 1970) is a Swedish radiologist from Vänersborg, who survived after a skiing accident in 1999 left her trapped under a layer of ice for 80 minutes in freezing water. During this time she became a victim of extreme hypothermia and her body temperature decreased to 13.7 °C (56.7 °F), one of the lowest survived body temperatures ever recorded in a human with accidental hypothermia. Bågenholm was able to find an air pocket under the ice, but suffered circulatory arrest after 40 minutes in the water.
After rescue, Bågenholm was transported by helicopter to the Tromsø University Hospital, where a team of more than a hundred doctors and nurses worked in shifts for nine hours to save her life. Bågenholm woke up ten days after the accident, paralyzed from the neck down and subsequently spent two months recovering in an intensive care unit. Although she has made an almost full recovery from the incident, late in 2009 she was still suffering from minor symptoms in hands and feet related to nerve injury. Bågenholm's case has been discussed in the leading British medical journal The Lancet, and in medical textbooks.
It gets more interesting at the Ressuscitation and Recovery section.
Bågenholm arrived at the hospital at 21:10. Her body temperature at the time was 13.7 °C (56.7 °F) (...) The electrocardiogram connected to her showed no signs of life, but Gilbert knew patients should be "warmed up before you declare them dead".
Bågenholm was brought to the operating theatre, where a team of more than a hundred doctors and nurses worked in shifts for nine hours to save her life. At 21:40, she was connected to a cardiopulmonary bypass machine that warmed up her blood outside of her body before it was reinserted into her veins. Bågenholm's first heart beat was recorded at 22:15, and her body temperature had risen to 36.4 °C (97.5 °F) at 0:49. Bågenholm's lung function deteriorated at 02:20, and she spent the following 35 days connected to a ventilator.
Bågenholm soon began to show signs of vitality, and woke up paralyzed from the neck down on 30 May. She feared she would spend the rest of her life on her back, and was angry with her colleagues for saving her. Bågenholm soon recovered from the paralysis, however, and later apologized to her friends; "I was very irritated when I realized they had saved me. I feared a meaningless life, without any dignity. Now I am very happy to be alive and want to apologize." Bågenholm's kidneys and digestive system were not working properly, so she had to recover in an intensive care unit for two more months.
Seems like she never described what it was to wake up like that with more elaboration than what is in the wiki. From that I conclude that it's like the hangover you get from drinking bootleg vodka, only you take a hundred days to recover instead of just twelve hours. Also you need a [redacted] expensive plan for health insurance.