I’m doing this on the Raspberry Pi, but you can do the same thing on almost any computer that exists. All you need is a web browser (like Firefox or Internet Explorer) and a text editor (like Notepad or Gedit).
If this looks very difficult, try the video I made making a similar card using Scratch, which is a lot easier: Snowflake Christmas card in Scratch on the Raspberry Pi.
If you’d like to use the snowflake picture I drew, right-click this link and choose “Save link as…” or similar: snowflake.svg.
If you’d like to compare my code against yours, right-click this link and choose “Save link as…” or similar: snowflakes.html.
If you’d like to see what the finished product looks like, just left-click on snowflakes.html above, instead of right-clicking.