Edit in JSFiddle

//Notice how some of the images are repeated? That's handy for increasing the frequency of some types of snow flakes.

//And, here's the source:
 // jSnow, a jQuery Plugin v1.1.mod1  
 // Licensed under GPL licenses.  
 // Copyright (C) 2009 Nikos "DuMmWiaM" Kontis, dummwiam@gmail.com  
 // http://www.DuMmWiaM.com/jSnow  
 // Modified 2009~  
 (function ($) {  
   $.fn.jSnow = function (h) {  
     var j = $.extend({},  
     $.fn.jSnow.defaults, h);  
     var k, WIN_HEIGHT;  
     setWaH();  
     var l = j.flakes;  
     var m = j.flakeCode;  
     var n = j.flakeColor;  
     var o = j.flakeMinSize;  
     var p = j.flakeMaxSize;  
     var q = j.fallingSpeedMin;  
     var r = j.fallingSpeedMax;  
     var s = j.interval;  
     var t = j.zIndex;  
     var useGif = false;  
     var u = $("<div \/>");  
     u.css({  
       width: k + "px",  
       height: 1,  
       display: "block",  
       overflow: "visible",  
       position: "absolute",  
       top: $("html").scrollTop() + 1 + "px",  
       left: "1px",  
       zIndex: t  
     });  
     $("body").prepend(u).css({  
       height: "100%"  
     });  
     $("html").css({  
       "overflow-y": "scroll",  
       "overflow-x": "hidden"  
     });    var v = Array();  
     generateFlake(l, false);  
     setInterval(animateFlakes, s);  
     window.onresize = setWaH;  
     function setWaH() {  
       k = $('body').width();  
       WIN_HEIGHT = window.innerHeight || document.documentElement.clientHeight  
       WIN_HEIGHT -= 50;  
     };  
     window.onscroll = function () {  
       u.css({  
         top: $("html").scrollTop() + "px"  
       })  
     };  
     function generateFlake(a, b) {  
       a = a || 1;  
       b = b || false;  
       var i = 0;  
       for (i = 0; i < a; i++) {  
         var c = $("<span \/>");  
         var d = o + Math.floor(Math.random() * p);  
         var e = m[Math.floor(Math.random() * m.length)];  
         if (e.indexOf(".gif") != -1 || e.indexOf(".png") != -1) {  
           var f = new Image();  
           if (useGif)  
             e = e.replace("png", "gif");  
           f.src = e;
           e = "<img src='" + e + "' alt='jSnowFlake'>"
         }  
         c.html(e).css({  
           color: n[Math.floor(Math.random() * n.length)],  
           fontSize: d + "px",  
           display: "block",  
           position: "absolute",  
           cursor: "default",  
           "z-index": t  
         });  
         $(u).append(c);  
         f_left = Math.floor(Math.random() * (k - c.width() - 50)) + 25;  
         f_top = (b) ? -1 * c.height() : Math.floor(Math.random() * (WIN_HEIGHT - 50));  
         var g = Math.floor(Math.random() * 90);  
         jQuery.data(c, "posData", {  
           top: f_top,  
           left: f_left,  
           rad: Math.random() * 50,  
           i: Math.ceil(q + Math.random() * (r - q)),  
           swingRange: g  
         });  
         c.css({  
           top: f_top + "px",  
           left: f_left + "px"  
         });  
         v.push(c)  
       }  
     };  
     function animateFlakes() {  
       var i = 0;  
       for (i = v.length - 1; i >= 0; i--) {  
         var f = v[i];  
         var a = jQuery.data(f, "posData");  
         a.top += a.i;  
         var b = Number();  
         b = Math.cos((a.rad / 180) * Math.PI);  
         a.rad += 2;  
         var X = a.left - b * a.swingRange;  
         f.css({  
           top: a.top + "px",  
           left: X + "px"  
         });  
         if (a.top > WIN_HEIGHT) {  
           jQuery.removeData(f);  
           f.remove();  
           v.splice(i, 1);  
           generateFlake(1, true)  
         }  
       }  
     };  
     return this  
   };  
   $.fn.jSnow.defaults = {  
     flakes: 30,  
     fallingSpeedMin: 1,  
     fallingSpeedMax: 3,  
     flakeMaxSize: 20,  
     flakeMinSize: 10,  
     flakeCode: ["&bull;"],  
     flakeColor: ["#fff"],  
     zIndex: "auto",  
     interval: 50  
   }  
 })(jQuery); 
 
    $(function() {  
     $().jSnow({  
       flakes : 25,  
       flakeCode : [  
         //"/img/jsnow/snow.1.png"
         '❄', '❄', '*'
       ],  
       fallingSpeedMax : 2,  
       fallingSpeedMin : 0,  
       zIndex : 65535,  
       interval : 30  
     });  
   });  

v.1.1.mod1

body{background: #679; color: #8ac;}