When you click on the scenery in Hearthstone, does your opponent see it?
When you click on the stuff around the board in Hearthstone, does your opponent see it happening too? For example, sometimes there is a church in the top left where you can break the windows.
No, only you see your clicks and effects on the game board's 'environment'.
However, there are some opponent's actions that are visible to you, e.g: minions on the battlefield or hero powers are highlighted when your opponent hovers their mouse over them.