Poetry in footnote

You could use a verse environment inside a minipage environment in order to suppress the unwanted initial blank lines. The following MWE illustrates this method. Since it appears you may have a lot of these cases, you may want to create a new command called, say \vfootnote, that acts like a normal footnote except that it typesets its contents in a minipage that's not offset very much -- per your stated preferences -- to the right of the footnote number

\documentclass{article}
\makeatletter
\newenvironment{fnverse}
    {\let\\\@centercr
     \list{}{\itemsep 0pt
     \itemindent   -1.5em%
     \listparindent\itemindent
     \rightmargin  \leftmargin
     \advance\leftmargin-1em}% adjust to taste
     \item\relax}
     {\endlist}
\makeatother
\newcommand{\vfootnote}[1]{%
    \footnote{%
    \begin{minipage}[t]{0.9\textwidth} 
    \begin{fnverse}
    #1 
    \end{fnverse}
    \end{minipage}}}

\begin{document}
\ldots\ the opening lines of Vergil's Aeneid.\vfootnote{%
Arma virumque cano, Troiae qui primus ab oris\\
Italiam, fato profugus, Laviniaque venit\\
litora, multum ille et terris iactatus et alto\\
vi superum saevae memorem Iunonis ob iram;\\
multa quoque et bello passus, dum conderet urbem, \\
inferretque deos Latio, genus unde Latinum,\\
Albanique patres, atque altae moenia Romae.}
More text \ldots
\end{document}

The resulting footnote looks like this (note that I've kept the page marker in the image to provide a sense of the vertical separation between footnote material and the page number):

An expansion of my earlier comment:

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{lipsum}
\usepackage[hang]{footmisc}
\setlength{\footnotemargin}{1em}% probably need at least 1.5em if >100
                                % footnotes
% default 'hang' values:
% \renewcommand{\hangfootparskip}{0.5\baselineskip}%
% \renewcommand{\hangfootparindent}{0em}

\begin{document}

Text.%
\footnote{\lipsum[1]}

\setcounter{footnote}{9}

Text.%
\footnote{\lipsum[1-2]}

\setcounter{footnote}{99}

Text.%
\footnote{\lipsum[3]}

\end{document}

In article.cls you can find the definition of \@makefntext:

\newcommand\@makefntext[1]{%
    \parindent 1em%
    \noindent
    \hb@[email protected]{\hss\@makefnmark}#1}

The following redefinition makes footnotes' lines aligned (basically we use hangindent for this:

\documentclass{article}
\makeatletter
\renewcommand\@makefntext[1]{%
    \hangindent=1.8em\hangafter=1\parindent=0em\noindent
    \everypar{\hangindent=1.8em\hangafter=1}% 
    \hb@[email protected]{\hss\@makefnmark}#1}
\makeatother
\begin{document}
In the Frost's
poem\footnote{%
Whose woods these are I think I know.\\
His house is in the village though;}
\end{document}