Q. Is there any truth to this statement:
That when Adam and Eve sinned their clothing was made from animal skins?

A. The verse (Bereshis 3: 21) reads: And Hashem G-d made for Adam and his wife garments of skin, and He clothed them. Rashi (ibid.) offers two Aggadic interpretations. The garments refers to a smooth fingernail or scale like covering attached to their skins or it could be a garment made from wool similar to the soft and warm wool from hares. Midrash Rabba (Bereshis 43) maintains that these were the desirable garments that Esav wore and then Rivka gave to Yaakov. Eventually they became the Cohen Gadol’s vestments.
The Talmud (Sota 14a) presents a disagreement between Rav and Shmuel that Rashi explains to be, whether the garments were made of wool or linen.
Talmud (Avoda Zara 11b) mentions that the garments of Adam ended up in Rome, and were used in a peculiar rite performed every seventy years.
Rabenu Bachya (ibid.) describes the garments as being made from the skin of the multicoloured tachash, used in the building of the Mishkan.
Midrash Rabba (ibid.) quotes that in the Sefer Torah of Rabi Meir the word “or,” in “garments of or,” was spelled with the letter alef, meaning light. The Zohar explains that initially they were shiny holy spiritual garments of light that became only skin, after they sinned.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a