I am putting in a powered gate across my road. What size wire would I use? It is a 200yd run from the nearest power pole.

Is the Nearest Pole where the Service comes in, or several poles Many yards away.
What Operator are you Planning?
Electrical Motor(s), DC Motors that work off charged Batteries?
Solar May be the way to go, It constantly charges the Batterie(s).
Heavy usage?
Is it a Slide or Swing?
http://www.liftmaster.com/consumerweb/pages/productmodeldetail.aspx?modelId=1463

I was thinking about using a garage door opener and converting it for this ppurpose. Can you hook dc up to something like that using a solar pack and inverter? Most likely it will be a slide gate.

If not TOO set on your garage door plan, Mule makes a gate opener which is battery powered with solar backup

If Solar, you want to use DC Motors, I feel Inverters are inefficient.
It can be done, but needs more Solar surface, and More Batteries.