Minecraft – How to change the weather

Weather has not yet been implemented in Minecraft Pocket Edition. It will possibly be implemented in 0.11.0, according to the wiki. From the page on Snow:

[Snow] is unrenewable as weather has not been implemented yet [...]

A mod released in March of 2014 attempts to mimic weather. Here is a link to the post on the Minecraft forum.

Unfortunately, Minecraft: Pocket Edition does not support any in-game commands for the time being, therefore there are no commands for changing weather or time.

There is a mod for Pocket Edition, however, that adds commands in Single Player mode, and one command in it allows you to set the in-game time, though there does not seem to be one for weather. The mod is not even updated yet for 0.13.0.

The only way to do so might be with an external world-editing app, provided that you're using Android (don't know if iOS has them).