Ach, ponies/horses are quite frightened of lots of things - their own shadow, a paper bag, a polythene bag, a stick, a wheelbarrow, tractor, a person in a fluorescent jacket, silage wrap, a balloon - the list is quite literally endless. They learn through repetition that these things don't hurt them and become calm when passing them. I would imagine that no coercion but repetitive pressure-and-release type techniques have been used to acclimatise the ponies to the flames, which don't hurt them. No way would they go through them if they thought they would hurt them.
Generally, horses that have been trained using coercion are pretty bad-tempered and unpredictable. Not ones I would expect anyone to trust pulling a cart at speed over jumps between flaming poles.
Or perhaps I am all rather rosy-bespectacled about it all...