Remember, north Vietnam has four seasons while the south basically has only two, wet and dry. Wet season is south is normally from September through December.
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Anytime is actually good time for Vietnam due to its geographic north and south spread. In the south after January will be more dry, while up north cooler weather will dominate during winter times.
But it depends. In the South, including Saigon, the dry season is from December to April. The rest of the year it’s rainy especially in October when there can be flooding. That said, even in rainy season it may just rain hard for one hour a day and then be okay the rest of the day. The plus also is that after rains humidity goes way down. In the North, December and January can be pretty cold.