Thank you for the question. I am so very sorry to hear about the tragic loss of your horse. I hope I can give you some insight. ....
I believe it is highly doubtful that the vet drawing blood that day had anything to do with what happened.
1. If he was using a vacutainer tube, there is no way he could have injected air into a vein or artery. The vacutainers are set up as a vacuum (hence the name) and therefore only draw the blood out. It would have required a syringe with air in it for him to push air into a blood vessel.
2. The large amount of time between the blood draw and his tragic death. Even if there had been an embolus injected....it would have caused a problem very rapidly....within minutes.
Without a necropsy it is impossible to tell exactly what happened to your horse, here are some ideas based on my years of experience in practice...
1. A sudden and severe colic....yes these can happen. I have seen horses go from normal, to incredibly painful and distressed to dying within minutes if a part of their bowel becomes severely entrapped or obstructed and then ruptures. Kind of like a dog with a severe gastric bloat and volvulus.....Usually it takes much longer but their are severe cases with a rapid progression
2. A chordea tendinae rupture in the heart. Horses dont have heart attacks in the way people do......but older horses (especially if they have a known heart murmur) can have a weakened valve and sometimes suddenly, one of the pieces of tissue that anchors a valve will break causing a complete disruption of normal blood flow in the heart. This can kill them very quickly.
I am very sorry once again for the tragedy you endured with your horse. I hope this gives you some insight. Take care.