I have heard lots of "anecdotal evidence" (which means Mashpiyim telling over what they heard at private Yechidusim [private audiences]) that the Lubavitcher Rebbe wanted people (or Bochurim) to wear hats and jackets.
Is there any "written" source for this statement (such as a Sicha (even non-Muga) Letter, etc.)
About hats, the Rebbe comments in a footnote to one of his letters (Igros Kodesh, letter 3356, and from there in Sefer Haminhagim, p. 9) that it is normative chassidic practice to wear a double headcovering - a yarmulka under one's hat. (As R' Y.S. Ginsburg points out (Hiskashrus, no. 537), this formulation fits with the older European (and American) practice that everyone wore a hat anyway, so that the yarmulka was the "extra" covering; whereas nowadays we think of wearing a hat as something additional.)
R' Ginsburg notes, though, that this doesn't necessarily mean that one has to wear a hat all the time; indeed, the Rebbe himself, when studying privately, often did so wearing only a yarmulka.
Not sure about sources for jackets.
Looking in R. Michoel Seligson's new index of the Rebbe's talks and writings (highly recommended, btw), he references (under בגד) an account from 5729, printed in from Kfar Chabad magazine #700, about an elder chassid who put on a hat and jacket before opening the door for the Merkos shluchim; the Rebbe commented, when hearing this, that this chassid may be "[physically] far away, yet [spiritually] very near."
