Part of the reasons that cattle and pigs are done sans tranquilization is two fold. The first is that many tranquilizers are not approved by the FDA or USDA for use in those species due to residue. Many tranquilizers also cause adverse effects such as excessive salivation or bloat in ruminants. There is also an issue of the drugs taking 10 minutes or so to take effect during which these animals which are often unhandled are in close contact with humans and thus panic. This panic state can lead the to working through the drugs. These procedures are often done when the animal is a few weeks to months old. Its often done VERY quickly.
Horses tend to be handled more by people, as a result, it can create difficulty when catching them if done without tranquilization. Horses do not have the widespread prohibition on many drugs as they are not always classified as food animals. In addition, we often geld horses at an older age. Horses also tend to be more, lets say dramatic about injuries then cows. Cows are well known for getting infections, walling them off and continuing with life. Horses get infections, have immunologic melt downs, go septic and die.
While I am glad that Janna had a good experience with her horse. I would not do that to my horse nor would I advise the OP to do that. The OP has a horse that is difficult to catch and who has a long memory. Castration without sedation or analgesia is going make a LASTING impression on the OP's horse which would make that horse harder to handle in my opinion. I say this as the owner of a mare with a very long memory. Get some good credits in your horse experiences with people bank account before you make a a negative withdrawal.