Separate ground for gate opener control box?
Is it worth electrically isolating the control box of a gate opener from a well grounded steel fence? 


Sorry about being pedantic: don't mix up Ground (GND) and Protection Earth (PE). GND is the 0V reference and current return for your circuit. PE is not necessarily at the same potential, and the words "Earthed" and "Grounded" have different meanings. In this case we're talking about earthing.


  except the wires from the gate lock and the actuator, which are bolted or welded to the steel gate and fence. 


I'm sure the live mains wires for these are not bolted to the gate, so this must mean that along with the actuator wires there is a protection earth wire coming out of the control box, and this one is connected to the steel gate, correct?

In this case... I assume your house is earthed via a metal post into the soil. Now, if this post is copper and the fence posts are galvanized steel, and you connect them with a wire, humidity and acidity in the soil will turn this into a copper/zinc battery whose poles are both posts and with the soil acting as electrolyte. A stray current will flow into the Protection Earth wire between the two posts, and they will corrode. If your house has underground metal tubes for water and these are also earthed, then maybe they will corrode too. 

This is something one has to be aware of, so make sure you check before connecting the house's Protection Earth to the fence. No current should flow.

If the gate must be connected to the control box's protection earth... which makes sense since there is a mains power actuator in it... then if you have a stray current problem you can solve it with an insulation transformer.

EDIT


  The gate opener is powered by a 12v battery which is solar charged, not attached to mains power.


OK so that makes the above irrelevant.


  There is a wire labled "ground" coming from the control box. My main question is whether to connect it to the steel fence post or to a separate copper ground rod. 


Yes in this case you can connect it to the closest piece of fence, or the gate post.

If lightning hits the fence you want the circuit's ground to be at the same potential as the fence. If you connect this ground to an earthed rod then the zapped fence will be at high voltage while your controller's ground will be earthed.