You can type in a question environment (only with the development version)

\explain{} 

A simple example:

\begin{question}{explanation}
  Which has the highest elevation among the following?
  \begin{choices}
      \correctchoice{Sagarmatha}
      \wrongchoice{K2}
      \wrongchoice{Mont Blanc}
      \wrongchoice{Aconcagua}
  \end{choices}
  \explain{Sagarmatha which literally means `Head of sky' is the native name of
           Mount Everest, the highest mountain in the world.}
\end{question}

To install test version

sudo add-apt-repository ppa:alexis.bienvenue/test
sudo apt-get update
sudo apt-get install auto-multiple-choice

For open questions there is already an option@ answer=text@, for example:

\begin{question}{open}
Define \emph{inflation}.
\AMCOpen{lines=5,answer=some text here}{\wrongchoice[W]{w}\scoring{0}\wrongchoice[P]{p}\scoring{1}\correctchoice[C]{c}\scoring{2}}
\end{question}

However, this seems to only fill one line of the answer box, may not be entirely what you need.