The different seasons in Assassin's Creed Shadows offer different weather effects - but you shouldn't worry about them affecting your gameplay.
In an interview with Play magazine, Assassin's Creed Shadows art director Thierry Dansereau explains that Ubisoft didn't want the changing of the seasons "to be something that could be perceived as very negative or have a negative impact on how you play." Instead, any changes caused by the seasons will likely be limited to the animation level.
That might mean that Yasuke and Naoe might have to clamber through snowdrifts with a somewhat awkward gate during Winter or huddle from the rain during Fall. However, you won't encounter additional gameplay challenges - like guards tracking your footprints through the snow or slipping while climbing a rain-soaked wall - that you wouldn't come across in Spring or Summer.
All of those weather systems are just a hint of what's to come, it seems, as the weather tech that Ubisoft developed for Assassin's Creed Shadows will feature "in much more depth" in future games. All that new tech is part of why we've been waiting so long for an Assassin's Creed game set in Japan - Dansereau also explained that while the setting has been long-requested, 2024 is the right time for Assassin's Creed Shadows because all that time "allowed us to really develop the new-gen features" that Ubisoft needed to "fully exploit" its version of Japan - and settle on its Origins-sized map.