A 45-year-old woman is brought to the emergency department after being found unresponsive outdoors during a winter night. Her companions report she had consumed a significant amount of alcohol. On examination, her right foot is significantly edematous and erythematous, with numerous large, clear and some small hemorrhagic blisters on the dorsal aspect, extending to the toes. She exhibits diminished sensation to light touch and pain in the affected area, with a palpable but weak dorsalis pedis pulse. Capillary refill is sluggish. Her core body temperature is 35.2°C. Her lab results are notable for a White Blood Cell Count (WBC) of 14.5 x 10^9/L, Hemoglobin (Hgb) of 13.8 g/dL, Platelets of 250 x 10^9/L, Sodium of 138 mEq/L, Potassium of 4.1 mEq/L, Glucose of 98 mg/dL, and Creatinine of 0.9 mg/dL. Given this presentation, what is the most likely diagnosis, and what is the immediate priority in her management?