Problem when applying foreach loop

In the \foreach variant, you are in a group when setting the dimension, so the "outside" value won't change. So you need to make the dimension global (or smuggle it out of the group). Here I made it global by just adding \global before \xmin=\x.

\documentclass[tikz]{standalone}
\usetikzlibrary{positioning}
\newdimen\x
\newdimen\xmin
\xmin=10000pt
\newdimen\y
\begin{document}
\begin{tikzpicture}[every node/.style={draw}]
\node (1) {182};
\node[below=of 1] (2) {183731468};
\node[below=of 2] (3) {74632};
\foreach \i in {1,2,3} {
    \path (\i.west); \pgfgetlastxy{\x}{\y}
    \ifdim\x<\xmin \global\xmin=\x \fi
    \fill[red] (\xmin,\y) circle (1pt);
}
\end{tikzpicture}
\end{document}

ADDENDUM: Of course, there are loops which do not introduce groups. The arguably simplest of those is the built-in \loop.

\documentclass[tikz]{standalone}
\usetikzlibrary{positioning}
\newdimen\x
\newdimen\xmin
\xmin=10000pt
\newdimen\y
\newcounter{loopi}
\begin{document}
\begin{tikzpicture}[every node/.style={draw}]
\node (1) {182};
\node[below=of 1] (2) {183731468};
\node[below=of 2] (3) {74632};
\setcounter{loopi}{0}
\loop
\stepcounter{loopi}
    \path (\number\value{loopi}.west); \pgfgetlastxy{\x}{\y}
    \ifdim\x<\xmin \xmin=\x \fi
    \fill[red] (\xmin,\y) circle (1pt);
\ifnum\number\value{loopi}<3\repeat
\end{tikzpicture}
\end{document}

You can use a different loop that doesn't do grouping. Instead of \i you use simply #1.

\documentclass[border=4]{standalone}
\usepackage{xparse}
\usepackage{tikz}

\usetikzlibrary{positioning}

\ExplSyntaxOn
\NewDocumentCommand{\nforeach}{mmm}
 {
  \cs_set:Nn \joulev_nforeach:n { #3 }
  \int_step_function:nnN { #1 } { #2 } \joulev_nforeach:n
 }
\ExplSyntaxOff

\newdimen\x
\newdimen\xmin
\newdimen\y

\begin{document}
\begin{tikzpicture}[every node/.style={draw}]
\xmin=10000pt
\node (1) {182};
\node[below=of 1] (2) {183731468};
\node[below=of 2] (3) {74632};
\nforeach{1}{3}{
  \path (#1.west); \pgfgetlastxy{\x}{\y}
  \ifdim\x<\xmin \xmin=\x \fi
  \fill[red] (\xmin,\y) circle (1pt);
}
\end{tikzpicture}
\end{document}