Well, ok, I wasn't trying to do it for you. I just did a quick job just to see if that was the effect you wanted...
Anyway, what I did was not the simplest way I'm sure, but here goes:
1: Open Paint Shop Pro and paste 6 iterations of the Jewelzz pic in there. So, you should now have 6 exact copies of the same pic.
2: Create a new image that is 300x600 (300 = image's width, 600 = your image's height times 4).
3: Using the pen tool, create snow droplets of different sizes, using whatever shape/color you want and fill the big image until it has the snow density you want.
4: Using the Magic Wand tool, select somewhere where there isn't snow. The whole page, minus the snow, should be selected.
5: Now, go to "Selections" and select "Invert Selection". Now, only the snow particles should be selected.
6: Copy that and paste it into the first Jewelzz picture (Edit -> Paste ->
"Paste as New Selection").
7: Position the snow's bottom edge to the pic's bottom edge. 1 down, 5 to go.
8: Do the same thing for each of the images, except move the snow down a little each time.
9: Once those are all done, save them all as GIF files somewhere.
10: Open Animation Shop and use the Animation wizard to paste in all those GIFs you saved. Set the speed to whatever you want.
11: Save the whole thing and you should be set.
You can create more than 6 images, reduce the amount of shift of snow for each pic, and increase the speed for a smoother animation.