Great question — answering as the UphillTech team:
You may be able to find inexpensive white buttons and sew them on. Those would be perfectly circular, of course, and would take just a little effort on your part. The trick would be positioning them so they look snowy. Another option would be to buy an iron-on t-shirt transfer sheet at an art store. They make opaque white sheets that can printed on with a home printer, and then ironed onto a shirt. If the shirt is smooth enough (not cable-knit, for example), you could cut small circles out of the white sheet and iron them on, following the instructions on the package.
Full answer by BrettFromLA: https://lifehacks.stackexchange.com/a/10213 (CC BY-SA 3.0).
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