How to construct a logic argument with colored hline with length under control?

You can use a simple tabular and colortbl:

\documentclass{article}
\usepackage{colortbl}
\usepackage{amsmath,amssymb}
\begin{document}
  \begin{tabular}{c@{\,}l@{}} 
                         & $p$ \\
\arrayrulecolor{blue}    & $p \to q$ \\\cline{2-2}
    $\therefore$         & $q$ \\
  \end{tabular}
\end{document}

You can change the color of the line using xcolor

\documentclass{article}
\usepackage{colortbl,xcolor}
\usepackage{amsmath,amssymb}
\begin{document}
  \begin{tabular}{c@{\,}l@{}} 
                         & $p$ \\
\arrayrulecolor{blue!60!green!70}    & $p \to q$ \\\cline{2-2}
    $\therefore$         & $q$ \\
  \end{tabular}
\end{document}

Same works with arrays also (since the MWE is given using arrays):

\documentclass[10pt]{article}
\usepackage{colortbl,xcolor}
\usepackage{newtxtext}
\usepackage{newtxmath}

\begin{document}
  $\begin{array}{c@{\,}l@{}}\arrayrulecolor{blue!60!green!70}
                & p         \\
                & p \to q   \\ \cline{2-2}
    \therefore  & q
  \end{array}$
\end{document}

I'd define an environment for this. Adjust the spacing (I used \enspace) and the color (here blue!50) to suit you.

\documentclass{article}
\usepackage{xcolor,colortbl,array,amssymb}

\newenvironment{deduction}
  {\begin{tabular}{@{}>{$}c<{$}@{\enspace}>{$}l<{$}@{}}\arrayrulecolor{blue!50}}
  {\end{tabular}}
\newcommand{\premise}[1]{&#1\\}
\newcommand{\conclusion}[1]{\cline{2-2}\therefore&#1}

\begin{document}
\begin{deduction}
\premise{p}
\premise{p\to q}
\conclusion{q}
\end{deduction}
\end{document}

Another possible solution:

\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath,amssymb}

\newcommand{\tikzmark}[1]{\tikz[overlay,remember picture] \node[yshift=-0.2ex]({#1}) {};}

\newcommand{\tikzhline}[3][1]{\tikz[overlay,remember picture]\draw[thick,cyan,shorten <=-{#1}pt,shorten >=-{#1}pt](#2.south)--(#3.south);}

\begin{document}
\[
\begin{array}{r@{\extracolsep{5pt}}l}
& p\\
& \tikzmark{a}p\rightarrow q\tikzmark{b}\\
\tikzhline{a}{b}
\therefore & q
\end{array}
\hspace*{0.5cm}
\begin{array}{r@{\extracolsep{7pt}}l}
& p\\
& \tikzmark{c}p\rightarrow q\tikzmark{d}\\
\tikzhline[6]{c}{d}
\therefore & q
\end{array}
\]
\end{document}

The result:

You will control the length by means of the optional parameter of \tikzhline.