Nepal has varied terrain and climate. Hence, you can trek in Nepal in any season. You just need to choose your treks right and buy gears accordingly. However, Autumn seems to be the best time to trek in Nepal based on overall weather and popularity.
Autumn lasts from September to November. The weather at this time of year is perfect, there is no or minimal rain and the weather is clear. This means the view of mountains during this time is spectacular.
The temperature is moderate. Short storms may add snow to high altitudes. Monsoon would have cleared the dust from atmosphere.
September is the peak month for trekking in Nepal.