Wow, what a great response. Thank you. 
What I really like is the horse?s general attitude. There is just something about it.
In terms of green, to give you an example, it would mildly mess about standing still at mounting block, stopped when checked. Though on the second viewing the woman showing the horse produced pasture mix magically from pocket by way of motivation to stand.
More experienced DH view of this is, it's probably trainable, but could be a pain in the @rse. Stables view ? it?s an Irish horse, they tend not to use mounting block.
I'm more inclined to agree with DH. I had Irish hunter before (slightly older) and could climb on from anything, including gates if the need arose, she would happily stand still.
By way of a stupid example about attitude, first viewing, when person showing got on, horse stepped over little step ladder thing they were using as mounting block and knocked it over. Reaction to this was very laid back, no jumping or spooking, snorting - which would have been justified for many. Just kind of look at it as if to say "oh, didn't know that was there". Then stood still when mounting stepladder repositioned and stood still for the woman to get on, and trundle off quite happily when asked.
On second viewing, there was a competition on at the place where the horse was being sold. Lots of horses coming and going, show jumping, hooter going off, etc. We walked and trotted passed the main school where the jumping was going on, horses coming and going, quad bike with leveller on the back rattling and bouncing across yard; horse didn't bat an eyelid. We took it around the lorry park. Trailers and cars coming and going, horses tied to horse boxes, horse lorrys parked, ramps being lowered, cars towing trailers starting up and leaving, etc. Didn't bat an eyelid at this either. We did this three times with three different riders: person showing, me, DH. Only point that horse quibbled was when third rider set off. Little bit of stepping to one side then the other when setting off, DH asked horse to go forwards, slighter stronger leg aids - and horse move forward and didn't quibble again. Moved in a direction away from the stables and other horse without any hesitation and going back in the direction of stables stayed at same speed, no getting faster or flustered.
However, and this is where the vet said the horse seemed green (a part from lunging), for the vet horse was very quiet to handle in stable, and willing to have feet picked up and was the same for me when I tried, but after being ridden and trotted up, etc the vet tried to pick its feet up again to look at shoeing, and it messed around quite a lot, got a bit stressed, in his words. But vet said, to be fair, that there was a pony in a field nearby charging around by way of distraction and upset. And if it doesn't know much about lunging, this may have also unsettled it.
Sorry this is turning into a bit of an essay. 
Last night I was determined I was going to walk away, then I spoke to DH and he confused me. He said I looked very comfortable when riding this particular horse, and that the horse reminded him of my old horse in terms of movement, way I rode it and attitude. I agree with this, and I think that's why I have such a "thing" for this particular horse. But I?m not sure if being like my old horse is the best motivation for being hung up on a horse.
I'm considering waiting until the horse is re-shod and then setting the vet out again.