What would the climate be like in the D&D 5e Saltmarsh area described in Ghosts of Saltmarsh? What would winters be like in terms of cold and snow? Would there be a rain season?
Saltmarsh is traditionally, and currently, placed in Gary Gygax's World of Greyhawk setting; on the continent of Oerik, on the sub-continent of the Flanaess, on the coast of the Kingdom of Keoland. First I'll look at the 1980 World of Greyhawk Gazetteer (Folio) for an overview (p. 5):
CLIMATE AND SEASONS
The Flanaess is particularly blessed in regard to its weather. Except in the northern latitudes, the winter temperatures seldom dip below freezing except during the two winter months-and at night during early spring and late autumn. In the depths of winter, there will be a few days of zero range temperature, and then gradual warming begins. The northeast and central northern regions tend to be considerably colder, the seas of those regions causing winter to linger about twice as long. An important exception to this is the Dramidj Ocean, whose warm currents tend to moderate the climate of the lands which border it to a degree similar to several latitudes further south. Both spring and autumn are protracted seasons, by and large. Summer in the central lands of Oerik lasts five or more months.
Prevailing winds tend to be from the northeast in the winter and autumn, from the east and southeast in other times. Most areas of the Flanaess have sufficient rainfall to assure abundant crops.
Keoland is in the southwest of the Flanaess, so definitely not in the colder parts. Next I'll look at the original publication of Saltmarsh in 1981's Dungeon Module U1: The Sinister Secret of Saltmarsh, by Dave J. Browne and Don Turnbull (p. 3):
The Town is a small, respectable fishing town. The inhabitants are relatively sober, hard working and amiable. There are adequate facilities for justice and law-enforcement—debtors and bankrupts are dealt with particularly harshly. Fishing is the main industry but there are some tiny farms in the neighbouring countryside. The town boasts a small weekly market to which traders are attracted from two larger towns, Burle and Seaton, each some twenty miles away (Burle inland to the northwest, Seaton along the coast to the east). In general, be guided by any small south-coast English fishing town of the 14th Century and with population about 2,000. On the WORLD OF GREYHAWK™ map, Saltmarsh is placed in the southernmost part of Keoland, at the western edge of hex U4/123.
Note the U-series which first presented Saltmarsh was the first series of adventures produced by TSR UK, which was prominently noted at the time. From the Preface:
It is with a great deal of pride that I introduce this module, not simply because it is partially my own work but also because it is the first AD&D™ module to have been written in the United Kingdom... it is an English module and it would be less than representative if it did not carry something of that atmosphere.
So it seems quite likely that the original authors' intent was for the climate of Saltmarsh to be a simulation of that on the English south coast.
Possibly in distinction to that, a full, fairly complicated, mechanical system for determining daily weather in the World of Greyhawk (based on real-world climate data) was given in Dragon Magazine #68 (1982), later republished in the World of Greyhawk boxed set (1983). Based on the information there, Saltmarsh is at about 23 degrees north latitude in that world; in the first and coldest month of Fireseek (analogous to January), the average daily base temperature would be 71 degrees Fahrenheit (about 22 Celsius) based on latitude and presumed warm-current seacoast location, and therefore under the rules there qualify as summer-like weather year-round; no chance of snow except in a severe record-low situation (at most 2% of winter days). In that respect, you can compare to Havana, Cuba in terms of real-world latitude. Precipitation is not radically more common in that system at any particular time of year; it varies smoothly from a high of 51% chance/day in Fireseek (January) to a low of 38% in Reaping (July), as per any seacoast location on the subcontinent.
Daniel R. Collins' citation of the World of Greyhawk Gazeteer is the most appropriate canon source for the climate and weather of Saltmarsh. I would note that what he cites as the "Boxed Set" is more specifically the World of Greyhawk Glossography (1983) from that set, which "contains a rewrite of David Axler's weather creation article from Dragon".
As far as the citation within U1 that DM's be "guided by any small south-coast English fishing town of the 14th Century", I think the preceding paragraph makes it clear that this is largely for cultural aspects, rather than climate.
Saltmarsh was later placed into the "Viscounty of Salinmoor" by fan work associated with the Living Greyhawk campaign and this was eventually canonized with the publication of the Living Greyhawk Gazeteer (2000). I think the most authoritative source for its climate would come from Gary Holian (lead author on the LGG), in his article "The Kingdom of Keoland" in the Living Greyhawk Journal. Here are some relevant quotes:
The land and its environs are often described as gloomy, helped in large part by the warm mists which waft off the nearby marshes south of Bale Keep and combine with the briny air of the sea to produce a persistent miasma. Fishing, including some whaling, dominates the local economy, which also sports small farms and some cattle grazing...The frequent storms which cross the Azure Sea south of Fairwind Isle to strike the western coast of the Sheldomar Valley often seem to hit this region the hardest.
For a real-world comparison, the humid subtropical climates of any of the US Gulf-coastal states would be good analogs. Snow would be unknown, but the constant high humidity would make winters feel cold to the natives (though not anyone from a more northerly clime). There would likely be a strong rainy season in the summer and dry season in the winter.