They are not the only nation who do not particularly travel with an animal guide. Earth Kingdom villagers, for instance, do not travel with a specific animal guide, but with pets. Many believe that badgermoles are Earth Kingdom animal guides, but the truth of the matter is that badgermoles do not like sunlight. Therefore, they cannot be domesticated unless in an environment lacking light. For instance, Earth Rumble Six, which is underground, uses a badgermole much like a zamboni. Fire Nation citizens, on the other hand, no longer travel with dragons, as they are thought to be extinct.
Water Tribesmen do not necessarily travel with animal guides as most species in both poles are specialists. The fauna in both tribes prefer colder climates, and as such, they cannot be brought out to locations like the Fire Nation or the Earth Kingdom.