I had problems with one of my horses (passport still registered to my old address) but the other was fine.
You have to 'associate' yourself with your horse and that will only work if your PIO has done their job and identified you as the owner in the first place.........
That's a problem with the information your PIO have provided to NED I think - I had the same problem with my 4yr olds passport. Might be worth a phone call to the passport folk to see that they have uploaded the right data?
I had a look for the horses at work and just about half were on there. POI is a mix of vetern horse society (Scrooge for come reason!) British Driving Society and Shetland Pony Studbook. Was told it's still all a work in progress and they should appear eventually