I don't know where this is written, but in Crawley-Boevey's notes (http://www1.maths.leeds.ac.uk/~pmtwc/quivlecs.pdf), there's a classification which is uniform for the different cases, and which should be easy to extend.  I believe the answer is just that you take one of the "obvious" representations over a finite extension of your field, and restrict scalars.  This shows that reps are classified by orbits under the absolute Galois group of representations of the algebraic closure of your field.  Note, this is really just taking seriously the idea that simple reps are classified (up to a few weird points) by points in $\mathbb{P}^1_k$.  For a non-algebraically closed fields, you have to include the points with residue field given by a finite extension.