Nepal has two distinct seasons, a dry one, which lasts from October to May, and a wet monsoonal one from June to September. The traditional trekking season is October to May. During the trekking season the nights can be very cold in the mountains, but the bright sun makes for pleasant day time temperatures up to about 25 degree Celsius, falling to 5 degree Celsius, at night, between 1000m and 3500m. At higher altitudes temperatures range from about 20 degree Celsius down to -10 degree Celsius. Mornings are usually clear, and then clouds can build up during the afternoon, disappearing at night to reveal spectacular starry skies.
After May, summer (Jun, Jul and Aug) is monsoon so visibility and rain are an issue. Mornings are usually clear with cloud build-up occasionally bringing afternoon rain. Treks can last from two days to a month or more, and the first consideration will be to choose a trek that fits into your available time and physical condition. You'll also need to strike a balance between trekking in the best weather for the area you wish to trek in and avoiding the crowds the good weather attracts.