Well you can sail in any season. The question remains whether you can afford the insurance premiums of doing so, to sort of paraphrase Fernand Braudel's "the Mediterranean, and the mediterranean world in Philip II's time" (1991), which I am currently slogging through in a Swedish translation.

Now in the Baltic it is somewhat more clear-cut. In many places you literally couldn't, as the gulf of Bothnia and the Gulf of Finland can and do freeze entirely over. Meaning that somewhere along the axle Stockholm-Tallin the sea is completely frozen over and even further south the shallower coastal water is like frozen too. This was a perennial problem for the Swedish state historically as it's main naval base resided at Stockholm whereas the Danes at Copenhagen had much earlier access to the sea. It took the Swedes until the late 1600s to move the main naval base to a more geographically advantageous position in the south of Sweden.

Somewhere around March and April is when the sea opens up except the most northern parts (of which no one really cared anyway, sue me reindeers). The fall ofc is the time of storms, I'm inclined to say soemwhere October-November is the latest you dare stay at sea, if that. I don't have the sources right here with me to check. It isn't all about weather either, to send your navy out you need to stock up on victuals too so even if you decide to risk it there are limits on how long you can stay out. And navies in the period, well later than medieval times as mediaeval times had limited navies, it was extremely risky to to push your luck as a freak storm could wipe out decades of military buildup.

Back to Braudel and the Mediterranean, he notes that during Roman times ships were laid up between October and April. He further describes a number of maritime cities' laws of the sea stipulated inactivity between 30.11 and 1.3 in Pisa 1160, Venice 1284 and Ancona 1387. From the 1400s people became "braver" and more inclined to voyage in the winter (in part because of new ships types), but 1569 Venice decided to reintroduce a ban on sailing between 15.11- 20.1 due to the number of shipwrecks. In 1561 and 1564 two different fleet admirals wrote to Philip II to protest his wanting to send the galley fleets out as they considered wintertime too dangerous. Even into the early 1800s fewer ships left Venice and Odessa in October (than previous months I assume the author means). A lot of this concerns galleys though, much more sensitive to weather. The northern roundship that was adopted around the 1400s and further developed in the mediterranean to become the classic caravel was much more able to survive the harder winter weather. This generally improved shipbuilding and seamanship so that a writer in the 1600s could note "on the Indian seas one doesn't sail all year round like we do in the Mediterranean". Braudel also looks at some statistics of shipping into ports, where such is available and that looks more even for a selection (not all years are available) 1578 - 1585 and there really isn't a significant change between summer and winter. Though these numbers exclude galleys and ofc come from a time when the roundship has more or less supplanted galleys as the main cargohauler. Trips do seem to take much longer in wintertime than summertime though in the Mediterranean at least.

Now all told as pertains to Europe (the Mediterranea, our side of the Atlantic, the Baltic), April through November seems to be the main sailing season. Outside of this you are pushing your luck. Although Braudel also notes that shorter trips could be done even outside this time if weather was good (unless you live somewhere the sea freezes at least). The earlier you go in the medieaval period the more constrained this "sailing window" likely was as ships and crews simply were not as good. A lot of this depends on the specific geography though. Am certain some places in the general area are specifically dangerous due to how climate and weather works at very specific times the locals would likely understand.