What is the Hotelling $T^2$ used for? Hotelling's $T^2$ distribution arises in testing differences between means of different populations. But is it often used? Can it be implemented in a modeling procedure, let's say, logistic regression?
 A: It is used to test means of different populations in a multivariate sense.  Hotelling's $T^{2}$ test is the multivariate analog of Student's $t$ test.  So, the 'mean' is in the sense of a mean vector.  
As far as logistic regression, I don't know.  Perhaps you mean a general linear model with a logistic link function, since a logistic regression is a univariate procedure.
A: Peter O'Brien has shown that logistic regression has several advantages over Hotelling's $T^2$.  You reverse the problem and predict group membership using as predictors the series of multivariate responses.  This does not require the multivariate normality assumption required of $T^2$, and allows mixtures of continuous and categorical responses.  If there is not just a difference in means but a difference in variance for a response across the groups, you include a square term in the logistic model for that response.  I suppose that if skewness differs you could include a cube term.
@ARTICLE{obr88com,
  author = {{O'Brien}, Peter C.},
  year = 1988,
  title = {Comparing two samples: {Extensions} of the $t$, rank-sum, and
          log-rank test},
  journal = JASA,
  volume = 83,
  pages = {52-61},
  annote = {see Hauck WW, Hyslop T, Anderson S (2000) Stat in Med 19:887-899}
}

