Question: I want this effect where it looks like snow/ rain is falling over a picture. Can I do that?

Yes! And not only can you do that, you can have lightning, too! 

So how is it done? With-- you guessed it-- the java applet. There are several places where you can get this applet online, like at Anfyteam and DS Effects (see below). Anfyteam offers the snow applet in its freeware collection of applets, while DS Effects offers both a rain and lightning applet. (The applets from DS Effects, however, come with a line of credit if they're not registered.)
 
 

Resources:

Anfyteam
Has a snow applet in its collection of freeware applets.

DS Effects
Like Anfyteam, this site offers a free snow applet in a collection of shareware applets. 

Java Boutique
Visit the index at this popular site to preview and download several snow applets.