Dan,
Your idea is a homemade DIY version of the
CheapHeat system for RVs by RV Comfort Systems.
It can be done, (especially if you are electrically inclined).
However, having fulltimed myself for over two years now, I can say that electricity is not the cheap way to go if your site is metered, and you need to pay for electricity separately.
It only makes sense if electricity is included in your site fee already, (usual short term RVPark or campsites).