Either cash when collected or bank transfer as late as you can before collection or possibly while you are there but that is not always an option, you need to agree the price maybe leave a deposit, get it vetted then arrange to collect as soon as you can with the money being exchanged before you take control of the pony, ie before you load it or the transporter does, don't forget to take out insurance before you pay, get a receipt and the passport.
Mine are cheap purchases and I don't vet them... turned up to view, paid and drove away with horse on the box
The few I've sold have been vetted, and then paid for at collection same/next day. I'd expect that kind of timescale though, if there was any kind of delay with picking it up then I would expect to hand over the cash as soon as I had decided to buy the horse I think, accepting that is a risk because you aren't in control...
1. a three hour journey away - offered deposit the day he passed the vet but this was declined, paid in full in euros cash when he was collected the following day.
2. from a riding school owner. I already had the pony on site, so when she passed vet I offered to bring round cash. Vendor said they preferred bank transfer, so this was done on the following day.
When I bought my boy the lady was on holiday so the yard staff were selling it for her I did a bank transfer and got a receipt to prove I had paid and she received the money before picking up him up the next day.