Over a number of weeks I would fill the arena, one by one, with obstacles - like in a pony club obstacle course. Tarp on the ground, traffic cones, post with flag tied to it, tyres on the ground etc etc.
Each weekly riding session with the horse I would be working on approaching/standing on/ walking past/ picking up etc the new obstacle in question.
I would set us up for success, never failure - start very very easy and never progress to fast.
My coaching to the owner would be along these lines
"Today we successfully walked past that traffic cone, she stopped when I asked, I leaned down and touched it with my hand, and then I asked her to move on. She is NOT scared of that traffic cone. I want you to repeat that exercise in hand, making sure that you control all the movement. Do not add anything else in! Little steps"
For me, this plan would (hopefully) work because:
It would give me the opportunity to find out how to get the mare near to or over things she doesn't like. Getting to deal with scary obstacles in a controlled environment is a very useful technique.
It would give the mare and the owner a structured program for gaining confidence in each other.
It should engage that Welsh Mare's clever little brain
I would be less concerned with making this mare produce good flatwork, and very motivated with making her use her brain in partnership with the human.