If you're snowed in, it may feel like there aren't enough things you can do with your preschooler or pre-preschooler to keep them entertained. Luckily, scribbling and drawing, which are fun and creative, also happen to build writing skills!
Writing and reading are bound together very closely - the skills support each other. When a child learns to write, they are learning about the shapes of letters and how they fit together, as well as developing skills in problem solving, creative thinking, and expressing their opinions and thoughts - and then translating that into symbols! You can't expect your preschooler or toddler to be writing yet, but you can support them by developing pre-writing skills through drawing, scribbling, and more. (You can read some very thick academic research on it here)
Here are some tips and ideas:
Storytelling - have your child tell you a story while you dictate it and write it down. That shows that their words have corresponding symbols on a page that make sentences.
Play post office! Set up letter writing materials, glue, and some fun found materials for stamps. Have them write a letter to you (even if it's just scribbles) and write a letter to them. Put it in an envelope, glue the "stamp" on, and exchange letters, asking them what their letter said and reading your letter to them.
Try just setting out some art supplies and paper and see where it goes. Spread out big sheets of paper for "giant drawing" on the floor. Have fun!
Write your grocery list together! Write them simultaneously, letting your child copy your movements. Talk about what you want to cook and eat, using rich vocabulary.
Be encouraging of all efforts. Treat their writing and drawing seriously! Have them sign their artwork to practice writing their name.
Water painting - holding a brush or a pen is great hand-eye coordination practice. Give your child a paintbrush and a bucket of water and let them "paint" the bathtub, the porch, etc.
Encouraging preschoolers’ early writing efforts: https://www.childcareexchange.com/library/5019684.pdf
Art of Writing: http://www.earlyliteracylearning.org/cellpract_parent/toddler/collections/CELL_Todd_Scrib_Draw.pdf
Making Reading and Writing Meaningful: http://projectenlightenment.wcpss.net/parent_resources/Make_Read_Write_Meaningful.pdf