Sounds similar, but I'm 100% certain that I'm remembering it from a documentary, I wouldn't be surprised if they made a movie from it, but I don't remember the saliva thing.
One guy disappeared in snowy weather with a wife + baby. This was in north america, iirc, and for around a week. They took a wrong turn, ended up on some icy backroad and crashed. They waited with the car for a couple of days, but due to baby and lack of food/help, they decided to move. They...