Also... sometimes, cold-weather survival techniques developed in isolation don't translate to civil society very well.
It would be more effective as a technique to free hair frozen to something - when it's cold, humidity is a bad thing, staying dry is the thing to do. Air transmit heat poorly (hence insulated glazing), a wet fur no longer traps air between the hairs and will lose most of it's efficiency as insulation.
Sure it might give a short term impression of heat, but soon it will make things worse.