Well, I didn’t find any patterns in my search, either. But this could be the launch of your design career! It wouldn’t be too hard.
Get a piece of graph paper, or download one - http://www.tata-tatao.to/knit/matrix/e-index.html.
Then, do a gauge sample of your yarn - cotton, I’m assuming, so you’ll know how many stitches and rows per inch you’ll get. For the sake of discussion, we’ll say 5 stitches and rows per inch. If you wanted a 10" X 10" cloth, you’d need to cast on 50 stitches.
Knowing that, lay out your graph paper with 50 X 50 squares. If you want to do a border stitch (maybe garter stitch) then color in the rows you’ll purl and leave the knit rows plain. Then color in the blocks you’d need to do your motif. There are lots of charts available for snowflakes and snowmen on the web and you could use these as inspiration.
You can do this! And think how proud you’ll be. Be sure to post photos of the finished products.