High altitude weather can swing from pleasant to genuinely dangerous depending entirely on timing. Kilimanjaro and Mount Kenya follow the same broad rainfall cycle driving weather across the rest of East Africa, but at their elevation, the effects are magnified: minimal rain becomes the difference between a clear summit night and a genuinely hazardous one.
One clarification worth making explicit. The seasons on this page describe conditions on the mountain itself, at altitudes from around 1,800m up to 5,895m. That's a different system from the lowland safari season classification you'll find on our main timing guide, mountain weather and savanna weather don't always move together, so don't assume the two pages are describing the same calendar.