I climbed Kilimanjaro via the Lemosho Route during an 8 day / 7 night trek in late January 2014. On the whole the weather was good (sunny or overcast) but nights are cold.
I climbed whole route wearing long-sleeve quick dry shirt plus cotton long-sleeve shirt over it, long pants (zip-off for shorts) along with baseball cap. Early mornings sometimes wore a windbreaker.
Second night out in Shira Camp 1 I discovered that my sleeping bag (rated -10 C for comfort; - 15C for extreme) was not warm enough. Contributing factor may have been that I was alone in my 2-man tent. My sister and her climbing partner were in identical bags, with liners, in identical tent and were fine.
From Shira 1 we went to Moir Camp for a night and then down to Barranco Camp. I was coldest at Shira 1 and then started layering extra jackets on my bag at night which helped. If I go again (always a possibility), I will get a warmer bag or at least a thermal liner.
Coming down from Lava Tower / Sharks Tooth to Barranco Camp we had a mix of ice pellets, wet snow (melted on contact) and mostly rain. Wore gloves that afternoon to keep hands warm. Descendent to Karanga valley floor on the next day was also done in rain and can be treacherous.
Summit night and descent were done in cloudless skies and beautiful. Four layers on upper and lower body but never too hot.
Five days after our summit we noticed snow cover on top and were told by other groups that they had climbed in 3 - 4 inches (7 - 10 cm) of snow.