As long as the skinny wire to the solenoid is hooked up to the accessory wire, and all of the other wires are the bigger, more heavy duty wires, I think you've got it. But I'm not an expert at winches by a long way.

 

The shop manual for my Polaris 800 sportsman has a diagram of the winch hook-up so check what ever brand you ride's manual it might be there. Check with Warn, a winch is a winch they all hook up the same.

 

I just finished wiring up the same solenoid to my bike to control a snow plow. I connected the 2 inner posts to the battery they are marked with red and black markings, red positive, black negative. The outer 2 posts (blue and yellow markings) were connected to the winch. I didn't worry about the polarity of these winch connections, if it worked backward I'd would just switch them or do it at the control switch. Now for the switch, the common terminal was powered from the positive of the same battery that powers the winch. The other 2 switch terminals were connected to the smaller green and black wires coming out of the bottom of the solenoid. Reversing the connections to these green and black wires would reverse the operation of the winch.

You mentioned you are using a separate battery to power the switch, not sure if it will work.

I rushed this reply as just about to go to work, I can send some pictures later if needed. If you have any question please ask.

 

Don't use the accessory plug to power the winch. You'll either melt the connector/wiring or continuously blow the fuse.
Winches are meant to be wired directly to the battery via a relay switch.
Cheers
Alex