I will say that the best thing might be a reshoot, a difficult location to get to, but worth the effort.
That's why I suggested 2 exposures. The white point on each of the two could be made the same so there wouldn't be any "really tedious miniscule work".I get that this was just a rough, quick photoshop job to show him what you were talking about, but I really don't like that this made the snow that was in the shadows brighter than the snow that was in the sun. I think it'd take a lot of really tedious miniscule work to get the effect you're after in photoshop without it looking really fake like it does here. Just my noob opinion though. Also, if you're doing that to the top, you have to mirror the effect in the lake, which will be really annoying because the lake makes it to where it will be two separate jobs you're trying to match by eye.
That's why I suggested 2 exposures. The white point on each of the two could be made the same so there wouldn't be any "really tedious miniscule work".
As it is in his original, the shadowed snow is no where close to being white.
An issue I didn't address is the white balance in the shaded portion is different (cold, having a bluish color cast), than the white balance in the sunlit portion (warm).