I bought a piece of property that has a new gate and opener that has never been hooked up. The gate opener is 110v and is 350 feet from the house with no electric near it. Do I have to run wire 350 feet to the gate opener or is there a solar power converter that will operate the opener?

There is a company that does Solar Powered, but this stores in a battery, a good option if AC is not Available, The Motors are Low Voltage DC(12 or 24 Volt usually). Remote Controlled or however. Converting Sunlight to through Solar Panels, to Batteries, through Inverter to Gate is Not Efficient and More Expensive.
1 Company, GTO Pro make these, will see if I can find site.

Here they are:
Gate Operators by GTO/PROÆ (http://www.gtopro.com/pro-sl-2000.html)
They have the manuals and other Downloads.
Here's another on I was thinking of:
Tau Italia Pagina Home (http://www.tauitalia.com/en/home.php)