A particle effect weather system certainly exists, and such environmental effects as snow have been displayed. And where there is snow, there will likely be rain, and probably other assorted effects.

Early on it was speculated that Halo might operate like a simulation, with real-time cycles of day and night based on the geometry of the Halo system and a realistic physics system.

While the physics of Halo's engine are certainly quite advanced, there's been little reason to believe that at this point it takes into account such celestial events.