Well, an Electric Fence (Wooden Stakes) might be possible but normal ones that are higher and block the view are certainly not allowed.
The local authority says it has to fit into the landscape.
There are many other "rules" which dont exist outside of this wine growing region. (Look of the house, size, nothing modern looking etc...)
A mini fence around the trees as you said is possible and they shouldnt say a thing about that.
Before i buy the property i will ask if i could remove some of the trees.