Kilimanjaro is big enough to make its own weather, which is why forecasts for Moshi tell you very little about what's happening at 4,500 metres.
The zones, and what each one feels like
Rainforest, roughly 1,800 to 2,800 metres. Warm and humid, often in the high twenties, and it rains here more than anywhere else on the mountain whatever the season. Expect to walk in a wet jacket on day one.
Heath and moorland, 2,800 to 4,000. Cooler, clearer, hot in the sun and cold in the shade, often with cloud sitting below you in the afternoon. This is the pleasant part.
Alpine desert, 4,000 to 5,000. Bare rock and dust, fierce sun, bitter as soon as it goes in. Day and night can swing thirty degrees.
Arctic summit, above 5,000. Below freezing day and night. Summit night is commonly somewhere between minus five and minus twenty with wind on top of it.
The seasons
Two dry periods and two wet ones. Roughly, January and February are warm and clear. The long rains run through late March, April and May, and the mountain is wet, quiet and slippery. June to October is the long dry season, cold at night and the busiest time of year. November into mid-December brings the short rains, which are patchier and often only an afternoon shower.
There's more detail, including what each month is like for crowds, on the best time to climb page.
Climbing in the rainy season
People do, and it isn't madness. The paths are emptier, the forest is spectacular, and the rain is mostly a lower-mountain problem since much of it falls as snow or nothing at all higher up. Rongai, on the drier northern side, is the usual choice. You need genuinely waterproof kit and a tolerance for mud, and Marangu's huts suddenly look appealing.
What the weather doesn't do
It doesn't usually stop a climb. Guides go up in rain, cloud and snow. What weather changes is how pleasant the week is and how cold summit night gets, and it is never a reason to go faster.
Dress for all of it in one day
Layers, every day, in the daypack: you can genuinely be too hot and too cold within an hour. Sun protection matters more than people expect, because the sun at 5,000 metres burns through thin cloud and reflects off snow while the air around you is freezing.
Forecasts, and how much to trust them
Not much, past a day or two. A forecast for Moshi describes a town at around 800 metres and tells you very little about a camp at 4,600. Mountain forecasts for the summit exist and are better than nothing, though the mountain regularly ignores them. Pack for the full range regardless of what the week ahead looks like, because you cannot send for anything once you're through the gate.