I keep the originals as no way would I let anyone else have my horses passport unless for a very good reason - the ones where they are on livery and the YO does the vet visits etc - perfectly good reason for them to have them.
Our 3 are kept on a friends farm, I have the originals but I gave him a copy in case anyone from the council ever showed up demanding them - he could show the copies and say I could provide the originals within the hour were they needed.
I do take them with me to competitions but not if I'm going to the beach or lessons etc.
I have never heard of a yard needing them "for insurance" though.
The passport is NOT proof of ownership (just as the reg document of your car isnt - it just says who the keeper is) although leaving it with a third party/YO/YM is certainly not something I would do.
All I have ever asked for, or been asked for, is a photocopy of a horses insurance document to prove TP liability cover and a note of when vaccs are due plus a note of the horses freezemark number or brand in case of escape!.
Our YO has ours so if we are on holiday or cant be there in an emergency they have it. We have a great relationship with our YO though built over many years not sure I would have given a copy to someone I didnt know
Does every horse have to have a passport by law? As I read on defra website that if they don't, you cannot move them or expect to be able to do anything with them. Does that mean if you have a hairy pony in a field that doesn't ever come out, it doesn't need one. By the way, all mine do have passports, just think its principle of giving copies. Hmmm.