Here are two details from Viennese drawings, the first from 1816, and other from 1827.
We can assume a consistent style of dress in Vienna through the period of Schubert's adulthood, as Parisian fashions were dropped in 1815 (Congress of Vienna; end of the Napoleonic Wars) and then almost as quickly adopted again in 1830 (July Revolution).
Writing about Carneval 1826, Martha Wilmot (Mrs. William Bradford) describes in great detail a rather unusual costume ball that consisted of 12 very elaborate walking tableaux (she does not mention dancing but as she labels some of the tableaux "quadrilles" it is likely they danced as well as marched). In the paragraph about her own dress, she mentions "white satin shoes and broad flat pink saddle bows" (239). After the final tableau, however, general dancing started, and all characters, classes, and ages intermingled, in the most informal manner of the contredanse. At 2:00am a supper was served. The party was given by the British ambassador; Wilmot was the spouse of the embassy chaplain. (She reports that by request of the Emperor the entire series of tableaux was repeated in the palace the following evening and "the quadrilles for want of dancing Masters as Heralds to guide them, got into . . . glorious confusion" (240); also that "after the Imperial family had seen the quadrilles there was a little dancing in the Crown Prince's Apartment" (241).
Wilmot also mentions dancing in the context of a typical day for the children and their governess. (Wilmot, Blanche, and Catharine are the Bradfords' three children. ) Note particularly the promenade (the polonaise) that offers the characteristic formal close to a session of dancing (equivalent to the procession of couples waltzing about the room to a deutscher Tanz).
The governess "makes both Wilmot and Blanche say lessons twice a day, in french, then she can practice them in dancing, teach work, and superintend . . . their [dancing and] other Masters. She dresses them for dessert, and comes in with them. After sitting about half an hour, I get up and announce a ball; [the governess] then waltzes with Catharine while I play some excellent waltzes that I have got. Then she waltzes with Blanche, (in fun) who will be an exquisite dancer, the little manner of her in setting about it is so admirable. The Squire has his turn [and] when this is ended [he] leads out one in a polonaise, the others follow, and so they proceed to the nursery--after which they sup, tell stories, and the two youngest go to bed. (83)
Alas, this report is from September 1820, before Schubert's D365 was published, but as the Bradfords remained in Vienna till 1829, it is entirely possible that she "got" music of his and played it at some later time -- she reports that the family always had a (rented) pianoforte in the house.
[note added 5-19-10: the longevity of the polonaise as a formal or processional dance is attested by Barbara Boisit's reproduction of the sequence of dances (Tanzordnung) for the first ball of the Gesellschaft der Musikfreunde (1830): the evening was divided into two halves with an hour's rest inbetween -- the first was polonaise, waltz, waltz, cotillon and galop, waltz; the second shuffled the dances but kept the formal dance at the head: polonaise, waltz, cotillon and galop, waltz, cotillon and galop (158, illustration). The same organization's ball for 1847 was considerably more complex, but still placed the polonaise at the beginning of the first part: polonaise, waltz, waltz, quadrille, waltz, quadrille, waltz, quadrille, mazurka, quadrille, waltz. The second part consisted of waltz and polka, quadrille, waltz, quadrille, waltz, menuet (!), quadrille, waltz and polka (Legler and Kubik, 94 illustration).]
References.
Wilmot, Martha. Ed. by the Marchioness of Londonderry and H. M. Hyde. More letters from Martha Wilmot; impressions of Vienna, 1819-1829, relating her experiences in the brilliant cosmopolitan society of Vienna as the wife of the Rev. William Bradford, chaplain to the British embassy, during a period when Austria was the political and social centre of Europe, and including a journal of a tour in Italy and the Tyrol, and extracts from the diary of her elder daughter Catherine for 1829. London, Macmillan and co., limited, 1935.
Buxbaum, Gerda. Mode aus Wien, 1815-1938. Salzburg: Residenz Verlag, for the Hochschule für Angewandte Kunst in Wien, c1986.
Boisits, Barbara. "Der erste Ball der Gesellschaft der Musikfreunde in Wien im Jahre 1830." In Boisits, Barbara, and Klaus Hubmann. Tanz im Biedermeier: Ausdruck des Lebensgefühls einer Epoche, 151-166. Proceedings from the Symposium Musizierpraxis im Biedermeier: Tanzmusik im ländlichen und städtischen Bereich, Graz, Austria, 26.-27. März 2004. Series: Neue Beiträge zur Aufführungspraxis, vol. 6. Vienna : Mille Tre Verlag Robert Schächter, 2006.
Legler, Margit, and Reinhold Kubik, "Anmutige Verschlingungen. Tänze des Vormärz: Quellen – Notation – Ausführung." In Boisits, Barbara, and Klaus Hubmann, 89-131.