Okay, I've actually talked to Pokémon support about this, and they help with the game programming and coding, and this is what they said:
We are unable to comment on how weather is generated in your game, however, we do recommend avoiding any edits of your DS calendar and clock. This can add complications and errors in your game that are not always easily fixed.
The Question and Answer (Note, doesn't work, will add screenshot later.)
I asked because it was bugging me too, and I looked into the weather further. Weather is puzzling. I'll list the conditions that count as weather:
Rain, Sun, Hail, Sandstorm, and fog.
Bulbapedia actually states that there are a few different types of each weather. I'll write a paragraph about each.
Regular rain falls mainly on Routes 5, 6, 7, 8, 9, 11, 12, 13, 15, 16, 19, 20 in Unova (cycles based on current time), Virbank City (sometimes) Driftveil City (sometimes) Icirrus City (Spring and Summer).
Thunderstorms are from Tornadus and Thunderus.
Not in Gen V on the over world.
Light snow is in most western parts of Unova, Route 6, Route 7, and near Dragonspiral Tower (winter only for all).
Heavy snow is in Icirrus City and Route 8 sometimes during the winter.
Always on Route 4 and Desert Resort.
The Eastern Routes usually have fog, and can be removed by a trick or by making it your birthday. Giant Chasm has permanent fog as well.
A brief description of Gen V weather:
Generation V introduced seasons, which can affect the occurrence of weather in certain cities and routes. For instance, in Driftveil City, hail and snow are present only during the winter, while rain is common during the spring and autumn. The Pokémon Thundurus and Tornadus cause a storm on the route they are on, which is treated as rain in battle. Despite still being present on some routes, fog is no longer present in battles and cannot be removed via Defog.
From this, I noticed that everything is "sometimes" and "always" and "time/seasons". This implies that the pretty much all weather in Gen V is determined and limited by date and seasons, so some while snow can be in winter, it can't be in summer. Now, looking back to the support answer, they said that it is technically unknown, so when the seasons happen for the weather, the weather that generates is completely random hence the answer and "sometimes". The cities are the same for the Routes and locations.
Please leave comments so I can edit.
Hope this helps! :D
Source: Bulbapedia and the email.