I've seen nothing on plastic shoes vs steel shoes.
But I would like to see where you read Gordon's horses were shod ever two weeks, if at all.
There are large areas of Africa (and the world) that getting a horse shod isn't possible locally and he wasn't going to load down with the extra weight to carry shoes. That was why he elected to make the trip with unshod horses.
Make sure your reading about Gordon's ride, not some other.
From the linked page:
An Important Alternative View ! Late in 1970 I departed on a 20,000 kilometer horse trip that was to take me from Lesotho, Africa to Austria and take nearly two years. A great problem was that of horseshoes. Going North from southern Africa there is a long ride before reaching Kenya, where shoes are available. Carry enough shoes? Ouch! Much discussion arose, with the vast majority saying that the shoes were needed. Then I thought of all the wild horses and wondered how they got on without a Smithy to visit. Made up my mind to forego the shoes, with the riding fraternity calling me mad, stupid, and worse. But, no shoes for the horses! The decision taken, I went and bought horses in Lesotho where the vast majority are unshod. I looked for horses with black hooves (ed. Note - because of their legendary hardness). Eventually took one with a white hoof but it was soon relegated to carrying a light pack. The drill was to start the trip slowly and give the hooves time to get to their hardest. At the end of each day a mark was made on the hoof with a file, one inch up from the front of the hoof. To start with the marks were in the wrong direction as the hoof wore faster than it grew. In two months the hoof was strong enough for us to ride for eight hours on a daily basis. At one point in the north of Rhodesia (now Zimbabwe) we used strap-on shoes to protect the hooves where the ridge tops were broken volcanic rock. These (emergency) shoes would have been better if they were made with cloth ties instead of straps. But they did the job for the one day they were required. It may be of interest that after arriving in Germany, the horses were retired to a farm. The new owner insisted they should be shod and called in the smith. The blacksmith was unable to make any marks on the hooves with his rasp. In fact the horses were not shod for more than a year, until such time as the hoof had grown softer. After that, to keep the horse's hooves in shape the farrier used a grinder on the hard hooves. For the new owner could not afford the time to ride the horses enough to keep the hooves worn down. Gordon Naysmith
His book on the ride is interesting. It's mainly about the ride and things that happened to him during the trip and you could come away questioning his sanity. Not about the saddle, shoes, etc...., but about the where he elected to ride, because of some of the things that happened riding through dangerous areas (there's always some form of tribal war going on in Afirca or bandits, etc....).