The dry season from May to September is the best time to visit. Days are clearer and the dirt road up from Tingo is less treacherous. That said, Kuelap sits in cloud forest, and cloud and mist are present year-round — even in the dry season you are unlikely to get a fully clear day. Many visitors find the mist enhances rather than spoils the atmosphere, particularly in the early morning when it rises slowly over the ruins.
The wet season from November to April brings heavy rain that can make the road up difficult or impassable, and the site itself slippery underfoot. If you visit during this period, check local conditions first and wear waterproof clothing. Tours from Chachapoyas are more likely to be cancelled or delayed in the wet season.
Whatever time of year you go, arrive early. The site is quietest before the tour groups arrive from Chachapoyas around midday, and the morning light and mist make for the most memorable experience.