Recalling early years with my VIC-20 computer...
Add snow by painting individual pixels white. The first time can start with snow at row 1, column 1.
1) Paint every 20th pixel horizontally.
2) Skip 20 pixels down and repeat step 1.
3) Repeat the above many times.
4) Let the scene remain for a fraction of a second.
5) Add one row to the snow position.
6) Draw the next frame.
To create your own graphical icons you need to know how to store an image in memory, and how to retrieve it and draw it onscreen. Storing a color image requires more work than a black and white image. Draw a simple cartoonish picture of a sleigh. Break it up into pixels. Store it in memory. Paint it where the car would appear. Create a variable for storing its row and column position from frame to frame.