The effect currently suggests quite light snow, but it can be made to look heavier by duplicating the layer.
Go to Layer > Duplicate Layer and a copy of the fake snow layer will be placed above the original and you'll see that the snow seems heavier now.
You can play with the effect further by erasing parts of this new layer or adjusting the Opacity slider in the layers palette. If you want a fake blizzard, you could duplicate the layer again.
This tutorial shows a simple but effective technique for adding a fake snow effect to a photo using GIMP. You can use this technique to give a wintry feel to all sorts of images and this could be ideal for many of your festive projects.