How to schedule events based on game time

You can use a daylight sensor connected to a command block. However, as daylight sensors measure skylight, the daylight sensor can't have an opaque block over it.

Since in your case you want to change the weather when it is night time, you would use an inverted daylight sensor which emits redstone output when it is dark. Using 4 redstone connecting the daylight sensor to the command block should be enough for the command block to only activate once the sun has set.

Here are the daylight detector power levels from the wiki:

The wiki says this about inverted daylight sensors:

Specifically, it outputs a signal strength of 15 minus the current light level, meaning that an inverted daylight detector actually outputs a strength of 11 at midnight, if it has line of sight with the sky. The effects of shade are applied before inverting, so shade increases the signal strength when it isn't already full, and prevents it from reaching zero.