Hot branding, yes, is extremely painful, which is part of the reason it has fallen out of popular use on horses, although it is still used on many larger horse production ranches. It is also used very commonly on cattle.
I'm familiar with hot branding in cattle! I've helped do it and watched a number of times but always cringe when I smell the smeel of burning hair!! :(
I always wondered how they brand horses at the big studs.
I've branded many hundred head of cattle with a hot iron and many horses. The freeze branding is also painfull but the advantage is you can take them to a vet and have them tranqd before you freeze brand. When ya get burned through that hair and the hide starts burning it kind of smells like BBQ and makes ya hungry.