Yes, there are seasons. Yliakum still has an indirect connection to the planet surface, not only the light from the outer sun passes the Crystal, but also the temperatures still have influence to some degree. In the Character Creation, you can read about the ten months, as well as in the
"Yliakum Calendar" wiki page.
And Aramara is certainly right, the Dome is high enough to leave room for cloud growth. You can see the walls around the Eagle Bronze Doors disappear in haze.
@ carua: If you can enable weather in pslaunch (provided your graphic card is powerful enough to display it without too much delay), you can see some effects now and then: More or less heavy rain, sometimes even snow, slight mist to thick fog. But the system is rather random, and you can only have separate weather per sector, which means there may be snow in just one half of the East Passage... Unfortunately, changing the weather is a risky moment, some clients crash, others just lock up for a few seconds. And the rendering is often wrong, e.g. even slight haze during rain can completeny tint half of the screen in white or grey. Bugs to be fixed somewhere between CrystalSpace and PlaneShift.