As far as i know, most weather conditions except thunderstorms would be fine. High wind speeds are mainly problematic in takeoff and landing scenarios if you cannot face up-wind. But most airfields were just that, fields. Few fields had paved landing strips close to the front, but they rather had wide, closely packed lawns. In Flying Fury, James McCudden describes how these fields were prepared in the beginning of the war, when the front was moving very rapidly.

Prolonged rainfall might also have been a problem in case the field became too muddy for safe operation. Contrary to popular belief, these early flying machines were not particularly flimsy, some were even quite fast and well-designed, especially toward the end of the war.