The conflict between Snowball and Napoleon is ideologically-based, and almost impossible to resolve through mediation or other typical means. Snowball, an idealist, truly believes that with the participation of all animals a Utopia can result; Napoleon sees the inherent problems with Old Major's philosophy and decides to take advantage of the system for his own power.
Snowball also busied himself with organising the other animals into what he called Animal Committees.
Napoleon took no interest in Snowball's committees. He said that the education of the young was more important than anything that could be done for those who were already grown up.
(Orwell, Animal Farm, msxnet.org)
Napoleon never intended to play by the same rules, and so Snowball's naivety becomes his downfall. The culmination of their relationship comes when Napoleon tries to have Snowball killed by his trained dogs; this abuse of power is endemic to their essential differences. Without some higher power that is able to keep Napoleon in check, there are few other ways that the conflict could have been resolved.
One other possibility would be for someone -- possibly an uninvolved third-party -- to educate Snowball and make him more cynical about Napoleon's intentions. Up until the last, Snowball assumes that they are moving towards the same goals; he never considers that Napoleon will betray him. By giving Snowball a dose of healthy suspicion, it is possible that he could have developed his own strong following to deflect the dogs, at which point the conflict would change from private to public, between two equally-armed powers.