It’s a fascinating question. Msgr. Charles Pope takes an in depth view in his blog post at Community of Mission:
The climate in Palestine, both today and at the time of Jesus, has two distinct seasons. The wet or rainy season runs from the mid-October to the mid-April while the dry season lasts from the mid-June to mid-September. During the dry season rainfall is rare. Although it can get very hot during summer, it often does not feel that way. Cool breezes and low humidity are typical, making the summers quite pleasant, especially in areas directly on the coast or on the higher slopes of the hills. During these months it is almost always sunny and the sky cloudless. Rain rarely falls during the summer because of the dominance of high-pressure zones. This provides challenges for farmers, who have to develop special methods for trapping water during the rainy season. During rainy season, although it does not rain every day, there can be significant rains that cause periodic flooding. While it gets cool in the winter and at higher altitudes (areas near Jerusalem and Bethlehem can even see snow), this is rare and usually limited to brief periods during December and January. Although the Bible refers snow in the area, it is mostly mentioned as occurring in the mountains to the north near Mt. Hermon
Read more of Msgr. Pope’s post at his Community of Mission blog.