Brushing snow to terrain

Unity Engine
1

Hello,
I’ve just started with Unity. I was creating snow for my terrain but I couldn’t find a proper way to add “snow layer” with no collision so basically I just want to extra height to the terrain without collision for that extra height.
I already tried to duplicate the terrain and I removed the collision of duplicated terrain but that’s not probably very good idea since the terrain is big and duplicated terrain just lags it more.

Thanks in advance, I hope you understood what I tried to say.

2

Bumping for more information.
I also tried to create a plane as detail mesh and that way I tried to brush snow to the ground but it lags too much.
I want to add different amount of snow to different places so one big plane is not going to do it unless there is way to brush that plane. Snow must not have collision so does anyone have any tips for this?