Snow on transparent texture?

Hi, I am “working” on a Statue of a Cat where the Head should be covered
with Ice and on some parts there should be some snow on it.
Now I created the statue, got a stone texture and material on it.
Then I wanted to create the Ice on the Stone by using shrinkwrap modifier.
To this point it looks very well but now I got the problem that I have this
transparent material and want to add some snow on the head, the shoulders,…

Maybe you could give some ideas how to handle it. I already tried to get a
transparent texture on the ice and wanted to use texture paint mode
for painting some snow on it but nothing changed on the Texture.

I would be glad if you could help.

(Before I forget: I work with Cycles Renderer)