As i write this i can't see any of the other answers so please ignore me if this is the same as any others
You need to write back to her
Dear Mrs blank, thank you for your letter regarding my fence. As the fence belongs to me and is on my land, there is no legal requirement for me to paint the side of it that faces you. Although it is entirely my fence, i am willing to give you permission to paint your side as you like as long as it doesn't interfere with my side, but remind you that as it is my fence, i cannot guarantee how long i intend to keep it. Therefore if you paint it it is entirely at your own risk. if this solution is not acceptable to you i would suggest that you put up your own fence on your land, which of course you would be free to paint however you like, and then you wouldn't have to look at our fence that is unsatisfactory to you. You indicated yesterday that your deeds say i have to paint your side of the fence. if you could provide me with a copy of your deeds i would be willing to look at them, however my deeds say make no mention of this. I'm sorry if this is disappointing to you, but that is the legal position.
yours,
angry neighbour