The winter months of Chiang Mai are from November to January and these months have a very nice and cool temperature. But near the mountains is where the temperature can go as low as zero degrees.
The summer months of March, April and May can be really hot. The best time to visit Chiang Mai would be either the winter or the rainy season. The rainy season is from May to September and therefore you can expect short burst of refreshing showers at times.