1. Copy/Paste this code in NotePad
2. Save As... snow.js
3. Upload on your hosting
4. Add this code to your web-site

<script type="text/javascript" src="http://hosting_domain/snow.js"></script>

1. Finish

Also you can put this js from my free hosting, heres code:

<script type="text/javascript" src="http://boriskuzmanov.1sthost.org/sneg.js"></script>

if  ((document.getElementById) && 
window.addEventListener || window.attachEvent){

(function(){

//Configure here.

var num = 50;   //Number of flakes
var timer = 25; //setTimeout speed. Varies on different comps

//End.

var y = [];
var x = [];
var fall = [];
var theFlakes = [];
var sfs = [];
var step = [];
var currStep = [];
var h,w,r;
var d = document;
var pix = "px";
var domWw = (typeof window.innerWidth == "number");
var domSy = (typeof window.pageYOffset == "number");
var idx = d.getElementsByTagName('div').length;

if (d.documentElement.style && 
typeof d.documentElement.style.MozOpacity == "string")
num = 12;

for (i = 0; i < num; i++){
sfs[i] = Math.round(1 + Math.random() * 1);

document.write('<div id="flake'+(idx+i)+'" style="position:absolute;top:0px;left:0px;width:'
+sfs[i]+'px;height:'+sfs[i]+'px;background-color:#FFffff;font-size:'+sfs[i]+'px"><\/div>');

currStep[i] = 0;
fall[i] = (sfs[i] == 1)?
Math.round(2 + Math.random() * 2): Math.round(3 + Math.random() * 2);
step[i] = (sfs[i] == 1)?
0.05 + Math.random() * 0.1 : 0.05 + Math.random() * 0.05 ;
}

if (domWw) r = window;
else{ 
  if (d.documentElement && 
  typeof d.documentElement.clientWidth == "number" && 
  d.documentElement.clientWidth != 0)
  r = d.documentElement;
 else{ 
  if (d.body && 
  typeof d.body.clientWidth == "number")
  r = d.body;
 }
}

function winsize(){
var oh,sy,ow,sx,rh,rw;
if (domWw){
  if (d.documentElement && d.defaultView && 
  typeof d.defaultView.scrollMaxY == "number"){
  oh = d.documentElement.offsetHeight;
  sy = d.defaultView.scrollMaxY;
  ow = d.documentElement.offsetWidth;
  sx = d.defaultView.scrollMaxX;
  rh = oh-sy;
  rw = ow-sx;
 }
 else{
  rh = r.innerHeight;
  rw = r.innerWidth;
 }
h = rh - 2;  
w = rw - 2; 
}
else{
h = r.clientHeight - 2; 
w = r.clientWidth - 2; 
}
}

function scrl(yx){
var y,x;
if (domSy){
 y = r.pageYOffset;
 x = r.pageXOffset;
 }
else{
 y = r.scrollTop;
 x = r.scrollLeft;
 }
return (yx == 0)?y:x;
}

function snow(){
var dy,dx;

for (i = 0; i < num; i++){
 dy = fall[i];
 dx = fall[i] * Math.cos(currStep[i]);

 y[i]+=dy;
 x[i]+=dx; 

 if (x[i] >= w || y[i] >= h){
  y[i] = -10;
  x[i] = Math.round(Math.random() * w);
  fall[i] = (sfs[i] == 1)?
  Math.round(2 + Math.random() * 2): Math.round(3 + Math.random() * 2);
  step[i] = (sfs[i] == 1)?
  0.05 + Math.random() * 0.1 : 0.05 + Math.random() * 0.05 ;
 }

 theFlakes[i].top = y[i] + scrl(0) + pix;
 theFlakes[i].left = x[i] + scrl(1) + pix;

 currStep[i]+=step[i];
}
setTimeout(snow,timer);
}

function init(){
winsize();
for (i = 0; i < num; i++){
 theFlakes[i] = document.getElementById("flake"+(idx+i)).style;
 y[i] = Math.round(Math.random()*h);
 x[i] = Math.round(Math.random()*w);
}
snow();
}

if (window.addEventListener){
 window.addEventListener("resize",winsize,false);
 window.addEventListener("load",init,false);
}  
else if (window.attachEvent){
 window.attachEvent("onresize",winsize);
 window.attachEvent("onload",init);
} 

})();
}//End.