Havasu Canyon’s elevation make for relatively constant weather. Any time is a good time to visit Havasupai and just as the weather, the water holes, swimming pools, and creeks are pleasantly warm year-round.
Perhaps the only timing-obstacle would be your own availability. Summer expeditions are usually the busiest, so if you are looking for a less-cramped experience, choose a time in early spring or late fall.
…the real treat is off-season: not only are the crowds almost nonexistent, but the air is crisp and the trails fresh.