Shulchan Arukh, Yoreh De'ah 382:5

איסור נעילת הסנדל לאבל. ובו ה' סעיפים:
(אבל) אסור בנעילת הסנדל דוקא של עור אבל באנפליא של בגד או של גמי או של שער או של עץ מותר שאין מנעל אלא של עור ואם הוא של עץ ומחופה עור אסור: A mourner is forbidden to put on sandals [or shoes]¹M.K. 15b, derived from God’s command to Ezekiel, ‘And put thy shoes upon thy feet’ (Ez. XXIV, 17), whence we infer that for everyone else this is forbidden. only if [they are made] of leather, but a pair of shoes made of cloth,²Or felt. reeds, hair or wood, is permissible,³Rubber is also permissible — A.H. for an [ordinary] shoe is [usually made] of leather.⁴Derived from Yom Kippur where the same prohibition applies. Yoma 78b; O.Ḥ. § 614. Thus T.H. Although the mourner is forbidden to wear shoes, nevertheless, he may recite the morning benediction, ‘Blessed art Thou … who hast provided for all my needs’ (v. Siddur Morning Benedictions) — R.E.Z. Margolis (Laws of Mourning). However, if it [was made] of wood and covered over by leather, it is forbidden.

חיה מותרת לנעול כל ל' יום מפני שהצנה קשה לה: A woman after confinement⁵Likewise, one who is sick (although not dangerously ill — A.H.), or one who has a wound on his foot (O.Ḥ. § 614, 3) — ShaK. So too, a pregnant woman, if she fears the cold — A.H. is permitted to wear [leather-] shoes throughout the thirty days [of mourning] because the cold is harmful to her.⁶T.H., derived from Yom Kippur where the same ruling applies. Mishna, Yoma VIII, I and Gemara ibid. 78b.

כל אדם מותר לנעול במקום שיש סכנת עקרב: Every person [in mourning] is permitted to put on shoes where there is danger of [being attacked by] a scorpion.⁷T.H., derived from Yoma 78b. According to Mord. M.K. III end, where one must appear before a ruler during mourning and must wear shoes, the custom is to put some earth into the shoes. Hence, it follows that the same procedure should be adopted in the present ruling regarding danger, or in all cases where the mourner is obliged to wear shoes — TaZ.

אבל ומנודה שהיו מהלכים בדרך מותרים בנעילת הסנדל וכשיגיעו לעיר חולצין ויש מי שאומר שאם היא עיר שרובה עובדי כוכבים אין חולצין עד שיכנסו לרחוב היהודים: A mourner or an excommunicant who were walking on the road, are permitted to put on shoes, and when they reach the city they remove [them].⁸Sem(H). V, 12; Tosef. Ta‘an. I, 6; Ta‘an. 13a; Y.Ber. II, 7(5b) ; Y.Yoma VIII, 1(44d); Y.Ta‘an. I, 6(64c); Y.M.K. III, 5(82d) ; RIDBaZ to Yad, Ebel V, 6. There is, however, an authority who states that [in] a city, the majority of which, are Gentiles, one does not remove [his shoes] until he enters the Jewish quarters,⁹Lit. ‘the open place of the Jews.’ O.Ḥ. § 554, 17 Gloss and references. [or a Jewish house].¹⁰Thus Tur in O.Ḥ. ibid. Nowadays that we live amongst the Gentiles with no separate quarters of our own, one should not remove his shoes until he enters his courtyard — A.H.