fancyhdr (or alternative?) on first page only in documentclass letter

You could use package scrlayer. It redefines empty as layer page style. So you can declare a new layer and add this to page style empty:

\usepackage{scrlayer}
\DeclareNewLayer[
  foreground,
  textarea,
  contents={\includegraphics[height=1in, keepaspectratio=true]{kitty}}
]{letterimage}
\AddLayersToPageStyle{empty}{letterimage}

Code:

\documentclass[12pt]{letter}
\usepackage[margin=1.3in]{geometry}
\pagenumbering{gobble}
\usepackage
  [demo]% only for the example because I do not have the pictures
  {graphicx}
\usepackage{lipsum}% only for dummy text

\usepackage{scrlayer}
\DeclareNewLayer[
  foreground,
  textarea,
  contents={\includegraphics[height=1in, keepaspectratio=true]{kitty}}
]{letterimage}
\AddLayersToPageStyle{empty}{letterimage}

\address{\hfill 123 Fake St \\ \hfill Faketown \\ \hfill Fakelandia 54321}
\date{} 
\begin{document}
\begin{letter}{321 Ekaf St \\ Nwotekaf \\ Aidnalekaf 12345}
\opening{Dear You Guys:}
\lipsum[1-6]
\closing{Yours sincerely,\\
\fromsig{\includegraphics[scale=.2]{signature}} \\
\fromname{John Hancock}
}
\end{letter}
\end{document}

---

If there are other pages using page style empty too, you can define a new page style for the first page of the letter:

\usepackage{scrlayer}
\DeclareNewLayer[
  foreground,
  textarea,
  contents={\includegraphics[height=1in, keepaspectratio=true]{kitty}}
]{letterimage}
\DeclareNewPageStyleByLayers{letterfirstpage}{letterimage}

Then you can patch \opening to replace \thispagestyle{empty}:

\usepackage{xpatch}
\xpatchcmd\opening
  {\thispagestyle{empty}}{\thispagestyle{letterfirstpage}}
  {}{\PatchFailed}

Now it is possible to use page style empty for the other pages:

Code:

\documentclass[12pt]{letter}
\usepackage[margin=1.3in]{geometry}
%\pagenumbering{gobble}% <- removed
\usepackage
  [demo]% only for the example because I do not have the pictures
  {graphicx}
\usepackage{lipsum}% only for dummy text

\usepackage{scrlayer}
\DeclareNewLayer[
  foreground,
  textarea,
  contents={\includegraphics[height=1in, keepaspectratio=true]{kitty}}
]{letterimage}
\DeclareNewPageStyleByLayers{letterfirstpage}{letterimage}
\usepackage{xpatch}
\xpatchcmd\opening
  {\thispagestyle{empty}}{\thispagestyle{letterfirstpage}}
  {}{\PatchFailed}

\pagestyle{empty}% empty page style for the other pages

\address{\hfill 123 Fake St \\ \hfill Faketown \\ \hfill Fakelandia 54321}
\date{} 
\begin{document}
\begin{letter}{321 Ekaf St \\ Nwotekaf \\ Aidnalekaf 12345}
\opening{Dear You Guys:}
\lipsum[1-6]
\closing{Yours sincerely,\\
\fromsig{\includegraphics[scale=.2]{signature}} \\
\fromname{John Hancock}
}
\end{letter}
\end{document}

The result is the same as above.

A simple \raisebox with optional [0pt][0pt] to fool LaTeX will do:

\documentclass[12pt]{letter}
\usepackage[margin=1.3in]{geometry}
\pagenumbering{gobble}
\usepackage[demo]{graphicx}
\usepackage{fancyhdr}
\usepackage{lipsum}

\fancypagestyle{empty}{\fancyhf{}\fancyhead[L]{\raisebox{-\dimexpr 50pt+1in}[0pt][0pt]{\includegraphics[height=1in, keepaspectratio=true]{example-imagea}}}}
\renewcommand{\headrulewidth}{0pt}

\fancypagestyle{plain}{}
\pagestyle{plain}

\address{\hfill 123 Fake St \\ \hfill Faketown \\ \hfill Fakelandia 54321}

\date{}
\begin{document}
\thispagestyle{empty}
\begin{letter}{321 Ekaf St \\ Nwotekaf \\ Aidnalekaf 12345}
\opening{Dear You Guys:}

\pagestyle{plain}

\lipsum[1-6]

\closing{Yours sincerely,\\
\fromsig{\includegraphics[scale=0.2]{signature}} \\
\fromname{John Hancock}
}

\end{letter}
\end{document} 

You could use a highly configurable letter class like scrlttr2:

\documentclass[12pt,fromalign=right,fromlogo,backaddress=false]{scrlttr2}
\usepackage[margin=1.3in]{geometry}
\pagestyle{empty}
\usepackage{graphicx}
\usepackage{lipsum}

\setkomavar{fromname}{John Hancock}
\setkomavar{fromlogo}{\includegraphics[scale=0.2]{example-image-a}}
\setkomavar{fromaddress}{123 Fake St \\ Faketown \\ Fakelandia 54321}
\setkomavar{date}{}
\setkomavar{signature}{\includegraphics[height=2\baselineskip,width=4cm]{example-image}\\
 \usekomavar{fromname}
}
\let\raggedsignature\raggedright
\makeatletter
\@setplength{firstheadwidth}{\textwidth}
\@setplength{firstheadvpos}{\dimexpr\topmargin+1in\relax}
\@addtoplength{toaddrvpos}{-2cm}
\@setplength{toaddrhpos}{\dimexpr\oddsidemargin+1in\relax}
\@addtoplength{refvpos}{-4cm}
\@setplength{sigbeforevskip}{0pt}
\@setplength{sigindent}{.5\textwidth}
\makeatother

\begin{document}

\begin{letter}{321 Ekaf St \\ Nwotekaf \\ Aidnalekaf 12345}
\opening{Dear You Guys:}

\lipsum[1-6]

\closing{Yours sincerely}

\end{letter}
\end{document}

Instead of scrlttr2 you can also use a standard class or a KOMA-Script class and package scrletter. The package provides almost the same functionality like the class.