This is What Most Likely Happened to the Russian.
I could never understand how some would think he survived a flesh wound out in the middle of nowhere in freezing temperatures. Some would mention the car being gone. It does generate a mystery yet who could drive out for miles without a clear knowledge of their surroundings, all the while driving with a bleeding hole in their head? There's also the fact that if he had survived, we would have heard from Slava again.
But anyway...
After Paulie loses his shoe and catches up with Christopher - there is a shot of the pair from above, within a tree as if there being watched. This most likely is the Russian hiding in the tree which makes perfect sense since his footprints abruptly ended. Since we never heard from Slava regarding the matter, the Russian most likely died while hidden above in a tree.