Awww, yours looks much nicer. The page doesn’t specify a font so I guess it’s just using the default font of the browser (or, failing that, any font that contains the Unicode character; I would be surprised if many do). My default font is Helvetica Neue.
– edit: I did some digging around. There are a few fonts on my computer which contain a snowman. My browser uses (for whatever reason) Hiragino which is a family of Japanese fonts that comes standard with every Mac. Your nice snowman is the one in Arial Unicode. Here are all the snowmen on my system: http://dl.dropbox.com/u/4073000/snowmen.png
I'm seeing the MS Gothic Snowman from your screenshot with Opera 11 on Win XP. The Kozuka Snowman is cute. Thank you all for the fun with unicode and fonts :)
– edit: I did some digging around. There are a few fonts on my computer which contain a snowman. My browser uses (for whatever reason) Hiragino which is a family of Japanese fonts that comes standard with every Mac. Your nice snowman is the one in Arial Unicode. Here are all the snowmen on my system: http://dl.dropbox.com/u/4073000/snowmen.png