Nepal has two main trekking seasons. Autumn, from late September to November, brings clear skies after the monsoon and the sharpest mountain views. Spring, from March to May, is warmer, with rhododendron forests in bloom.
Winter, from December to February, is cold at altitude but clear and quiet, and good for lower treks like Poon Hill and for Kathmandu and Chitwan. The monsoon, from June to August, brings rain and cloud to the mountains, but valleys are green and trails are empty.
If you want helicopter flights, plan for the drier months and keep a spare day in Kathmandu in case the weather delays your flight.