It's quite hard. It's very hard to change the line breaking around a page break so the decorations would need to be added outside the normal text block, you can't really add the continuation marker within the existing lines. Probably the easiest way is to add a special strut 1sp larger than a normal strut into the end of the footnote, then if the footnote box does not have that depth you know it was split so can add the markers

\documentclass{article}
\makeatletter
\newdimen\ftnflag
\AtBeginDocument{{\footnotesize\selectfont\global\ftnflag\dp\strutbox\global\advance\ftnflag1sp\relax}}
\let\old@makefntext\@makefntext
\def\@makefntext#1{\old@makefntext
#1%
\dp\strutbox\ftnflag
\@finalstrut\strutbox}%
\gdef \@makecol {%
\ifvoid\footins
\setbox\@outputbox \box\@cclv
\else
\setbox\@outputbox \vbox {%
\boxmaxdepth \@maxdepth
\unvbox \@cclv
\vskip \skip\footins
\color@begingroup
\normalcolor
\footnoterule
\ifx\splitftn\vbox
\hbox{\smash{\raise-\baselineskip\hbox{\llap{$\rightarrow$}}}}%
\fi
\global\let\splitftn=\null\relax
\typeout{dp \the\dp\footins, dpstrut \the \dp\strutbox}%
\ifdim\dp\footins<\ftnflag
\global\let\splitftn=\vbox
\fi
\unvbox \footins
\ifx\splitftn\vbox
\nobreak
\vskip-\ftnflag
\hbox{\rlap{\kern\textwidth$\rightarrow$}}%
\else
\fi
\color@endgroup
}%
\fi
\let\@elt\relax
\xdef\@freelist{\@freelist\@midlist}%
\global \let \@midlist \@empty
\@combinefloats
\ifvbox\@kludgeins
\@makespecialcolbox
\else
\setbox\@outputbox \vbox to\@colht {%
\@texttop
\dimen@ \dp\@outputbox
\unvbox \@outputbox
\vskip -\dimen@
\@textbottom
}%
\fi
\global \maxdepth \@maxdepth
}
\makeatother
\addtolength\textheight{-10\baselineskip}
\def\a{One two three four five six. }
\def\b{\a\a Red green blue}
\def\c{\b\b\b\footnote{\itshape\b \roman{footnote}\b\a\b\b\b}\a\b\par A B C D \b\a\a\a\a\a\a\b}
\begin{document}
\c\c\c\a\b\c\c\c\b\a\c
\end{document}