Nepal, Sikkim, Garhwal
These areas of the Himalayas have four seasons: winter from December to February, Spring from March to May, Monsoon from June to August and Autumn from September to November. You can visit at any time of the year however the two main trekking seasons are Spring (also known as pre monsoon) and Autumn (also know as post monsoon).
October is the most popular trekking month in the Himalaya followed closely by November. These months normally have dry weather with clear blue skies and sun. It is possible to trek during December although of course the temperatures will be colder. Late February is at the tail end of winter with temperatures still cold at higher altitudes although this is a good time to visit to places at a lower elevation such as the Annapurna middle hills. As the year progresses into March and April the weather warms up, this is a good time to trek anywhere in Nepal especially as rhododendrons will be in flower in many places.
Pakistan and Ladakh
The trekking season for the Karakoram in Pakistan and Ladakh is during the summer. This is due to the area not being influenced by the monsoon to the same extent as Nepal and most of India. The season begins at the end of May and continues on to mid October however the best time for Snow Lake and Hispar La is July and for K2 & Gondogoro La is August.
Kilimanjaro
It is possible to climb Kilimanjaro at any time of the year however the two main climbing seasons are during the dry seasons from January through to mid March and early June to mid October. January through to mid March tends to be dry and warm, whereas June to mid October is generally cool and dry.
These are the general patterns on Kilimanjaro although the weather can often be unpredictable. It is possible to climb Kilimanjaro at any time of the year although it can be very wet and muddy in the rainforest in April and May.