The plow is on the front of your car right? Why can't you just route the power cable into your car before it goes to the plow and have a switch sitting along the wire in the cabin?
Or you could put the relay as close to the cabin as possible and run two small wires out with a switch sitting in the cabin to drive the coils on the power relay.
All the wireless stuff seems all for nothing, more work, and less reliable...Why do you even need wireless? If it was something on the back end like a trailer or somethign I would understand, but this thing is on the other side of the windshield.
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For the remote, you can get little keychain things like this:
**broken link removed**
You can have a 12V->5V regulator piggyback off of the power cable to power the receiver.
To switch the lights you can use a normall open relay, a two-way latched relay, or a MOSFET.
You *might* be able to get a MOSFET that can pass 25A and have a gate threshold voltage that is low enough to be driven by the receiver. Since I'm pretty sure the receiver output does not latch, you would need a latching circuit to continue to drive the FET after you release the button. Same thing goes for the normally open relay, except it's slightly more annoying because now you have to latch a larger current.
The relays function more reliably in cold temperatures (but it turns out you need a transistor to drive the relays anyways), but you need more current to switch them (and the normally open relay sucks power to keep the switch closed if it that matters in the grand scheme of things).
And then there is the issue of how to make the receiver and circuit rugged and withstand -36C temperatures. I think this is the biggest problem.