I created this little holiday card over a year ago with CSS3, luckily now I use Less, but here is the code for a snowfall animation using CSS transitions and keyframes. Use it however you like, including the image which I created using Adobe Illustrator.

Basically all you need to do is create some empty divs in your HTML and create circles in the css

    <div class="snowOne"></div>
    <div class="snowTwo"></div>
    <div class="snowThree"></div>
    <div class="snowFour"></div>
    <div class="snowFive"></div>
    <div class="snowSix"></div>
    <div class="snowTwo" id="moveTwo"></div>
    <div class="snowOne" id="moveOne"></div>
    <div class="snowThree" id="moveThree"></div>
    <div class="snowFive" id="moveFive"></div>
    <div class="snowOne" id="slowOne"></div>
    <div class="snowSix" id="moveSix"></div>

The trick is to start the animations at different times and angles yet they need to come from the same direction so it looks natural.