Question: In the winter when it is cold outside and there is condensation or frost on the window, may one use one’s finger to write or draw on the window?
Answer: One of the thirty-nine works forbidden by Torah law on Shabbat is writing. Nevertheless, our Sages teach us that the Torah prohibition of writing on Shabbat only applies when one writes something lasting, such as when one writes with a pen on paper, for such writing is certainly meant to last for a long time.
Nonetheless, the Mishnah (Shabbat 104b) and the Rishonim explain that our Sages prohibited writing even through a method that is not meant to last, such as writing with berry juice on a table and the like.
Thus, it is forbidden to write using one’s finger on sand or ash on Shabbat. It is likewise forbidden to write on a substance which is not meant to last for a long time, such as writing on an onion peel, which the Tosefta (Shabbat, Chapter 12) states is forbidden on Shabbat. Although according to Torah law, writing on an onion peel on Shabbat is permissible since the onion peel cannot last for a long time (as it will soon dry out and shrivel up), nevertheless, our Sages forbade even such writing on Shabbat.
Based on the above, one of the greatest Acharonim, the Peri Megadim (Mishbetzot Zahav, Chapter 340, Subsection 3) writes that one may not write letters with one’s finger on glass windows in the winter when there is condensation or frost on the window as a result of differences of the indoor and outdoor temperatures. Nevertheless, merely drawing a straight line on a frosty window is permissible on Shabbat, for this is not included in the kind of writing our Sages forbade. Maran Rabbeinu Ovadia Yosef zt”l rules likewise in his Chazon Ovadia-Shabbat, Volume 5, page 148.
Based on the above we can derive that the same applies to drawing, such as drawing a face or any other figure or picture one deliberately draws on the frosty window or on the glass of a dirty car window and the like is completely forbidden on Shabbat, for this is likewise included in the writing forbidden by the rabbinic enactment on Shabbat.
Nevertheless, wiping one’s finger across a completely clean and dry table or in the air in order to signal something to one’s friend is permissible on Shabbat, for this is not considered writing at all.
Summary: One may not write or draw on a window which has frost or condensation on it as a result of the cold outside. It is likewise forbidden to write or draw on a dirty glass window and the like.