The most important question is not if she has died, but what is the ambient temperature?
If it is very cold (below freezing) then death is not an immediate issue. The curious case of Anna Bagenholm proves our understanding of death leaves something to be desired. Anna had the misfortune of falling through ice and drowning. Her body temperature then plummeted and she was on face value clinically dead. But given the ambient temperature doctors managed to resuscitate her hours later.
There's the awful case of Frank Gardner, a BBC journalist shot and left for dead in Saudi Arabia. His life was saved, although he is now disabled and suffers chronic pain. Gardner's survival hinged upon the skill of the South African gunshot specialist surgeon in the hospital he was rushed to. Along with a number of drugs which were used to both stop the flow of blood from the wounds, and to stop his blood generally starting to clot (which occurs before death). The latter prevented multiple organ failure from concluding.
Gardner's injuries included multiple gunshots which had caused devastating internal injuries to the stomach and intestines. Surgery ended up removing some of his intestines and other organs. The severity of the injuries led to immediate complications, various infections which took weeks to heal with intensive care. In your case the injuries sound less problematic.
So long as she can get medical attention quickly the blood loss in itself is not a problem. There are various blood substitutes whose purpose is to carry oxygen instead of blood. But there have also been trials for new techniques which seem as exciting as ghoulish. One 2014 trial conducted by UPMC Presbyterian Hospital in Pittsburgh, Pennsylvania, USA, is worth mentioning and further reading.
The gist is that the patient who has suffered severe blood loss from violent trauma has all of their blood replaced with cooled saline solution. This drops their body temperature, which puts them into a medical coma and reduces metabolic function, essentially preventing the onset of decay, thus putting them in 'suspended animation'. Once they are in this state, they can be moved to a medical facility, their wounds fixed up, and then blood transfusions can occur and they can be resuscitated.
If the patient has access to the correct climate, drugs, medical techniques, then survival is very possible yes.