There are pros and cons to each choice. Overall, it is optimal to vet a horse BEFORE taking it on trial. It documents the condition of the horse before it enters your care and protects you as the buyer from being blamed for any issues that might show up. Also, it protects you from assuming the effort and risk of a trial with a horse that ends up failing a vetting. It also protects you from hard feelings from a seller who might be upset that you chose to return a horse from a trial (usually a seller should be okay with that since that’s the whole point of a trial, but sometimes people are funny).
Also, ideally purchase price should be agreed upon and and handed over (even if just to be held) while the horse is on trial. But, it’s possible that the vetting could discover an issue that might affect the value of the horse–something that’s not a deal breaker, but that might cause you to say to the seller, hey, I still want to buy him but I can only offer you X amount given the concerns related to X veterinary finding. It’s really awkward and difficult to negotiate if you have already have agreed on a purchase price and have the horse on trial.
Also, many sellers are not open to trials, and many trials require the hassle of contracts and insurance, again, enough hassle that you’d probably want to vet the horse first.
My advice is to make every effort to attend the vetting. If you cannot, be sure to use a reputable equine vet in that area that does not have any association with the seller. Also, you might be able to request something creative, such as having a vet tech or even the seller FaceTime you during key portions of the vetting. Definitely make sure you are immediately available by telephone during the vetting. On occasion, a serious issue will present quickly during the exam, and in this scenario you might wish to terminate the exam early to avoid the extra expense of a full exam and report. Be sure to schedule a private conversation with the vet (out of earshot of the seller) after the exam to review and discuss findings immediately after the exam.