1) Any activity which helps to remove dirt from a garment might be considered as ''Laundering'' - ''Kibus'' - and is prohibited as a derivative of ''Bleaching''. 2) Since feathers aren't embedded in the garment like water or dust, removing them isn't considered similar to ''Laundering''. Similarly, if snow hasn't melted yet, it's allowed to shake it off, because it's then similar to removing feathers.

1) There is a Rabbinical prohibition called ''Muktzah'' - ''Set Apart'' - which limits the objects one can move on Shabbat. See Ch. 88. 2) Wiping it on a stone wall looks like one is adding to or strengthening the wall, which is prohibited as a derivative of the Av Melacha (prototype prohibited activity) called ''Building'' - ''Binyan''. 3) The basis for this Rabbinical prohibition was a concern that one might wipe one's foot or shoe over a hole in the ground, thereby filling the hole, an act which would be prohibited under the Av Melacha called ''Ploughing'' - ''Choresh''; obviously this prohibition only applies to natural ground. The Mishna Berurah (302:28) writes that there are those Acharonim (Later Halachic Authorities) who permit wiping on both a wall and the ground, and there are those who rule that we should be stringent in both cases. He concludes by saying that in the case of wiping on a stone wall, one can certainly rely on those who are lenient, because most Rishonim (Early Authorities) permit it. 4) Soaking an absorbent fabric with water is considered part of the laundering process, and thus prohibited; so when pouring water on a shoe, one should be careful not to wet the stitching. 5) One of the 39 Avot Melachot (prototype prohibited activity) is smoothing out leather hides - ''Memachek''. Scraping the mud of a shoe with a knife, with force, would result in the smoothing of the leather surface to a certain extent, and is thus prohibited. If the mud is still moist, one may wipe it off with a rag or paper towel. If the mud is dry, it's forbidden to remove it in any manner, because it will crumble in the process, and resemble an act of ''Grinding'' - ''Tochen'' - which is one of the 39 Avot Melachot. Any activity that involves breaking down an item into small particles or pieces might be a derivative of ''Grinding'' - ''Tochen''.

טיט שעל רגלו או מנעליו יכול להסירו בדבר שמותר לטלטלו או שיקנחו בקורה אבל לא יקנחו לא בכותל ולא בקרקע ובשעת הדחק כגון שצואה על רגלו או על מנעליו ואין דבר שמותר לטלטלו יכול לקנח בכותל ואם אין כותל יקנח בקרקע ואם יש לו מים יכול לרחוץ המנעל גם במים אם הוא של עור כי בעור שכשוך בעלמא לא הוי כבוס אלא כשמשפשפו צד זה על צד זה כדרך הכובסים אבל בסכין אסור לגרור הטיט והצואה מן המנעל של עור והברזל שלפני הבית שעשוי לכך אם הוא חד אסור לגרוס בו ואם אינו חד מותר

) Any activity which involves removing dirt absorbed into a fabric, might be considered ''Kibus'' - ''laundering'' - which is prohibited as a derivative (Toldah) of Melaben - bleaching. Since the mud will make the towel unusable, and mud can be rinsed off easily, one might inadvertently rinse out the towel. It's permitted, however, to wipe up moist mud with a rag or paper towel, since one isn't disturbed by its becoming soiled, and will therefore not want to rinse off the mud (see Shulchan Aruch 302:11). However, one shouldn't wipe off dry mud, in any manner, because it resembles ''Grinding'' - ''Tochen''.