Adding snow to mountaintops

I started with an image of Sinopah Mountain in Glacier National Park on which I wanted to add snow to the mountaintop.  In so doing, the Generative Fill took quite a bit of the mountain away.  It did add some very good looking snow, but removed a good chunk of the mountaintop.  Then, I tried to add snow to the top of Never Laughs Mountain and the same thing happened.  Much of the mountain is removed from the selected area.  On Never Laughs Mountain, I got very little snow but lost quite a bit of mountain.  The file sizes are too large to leave as examples as the layers would be needed to see the changes.