If you want to run lights in your horse trailer using a battery that charges while the trailer is hooked up, it's generally a good idea to use a charge controller to regulate the charging process and ensure safe and efficient charging of the battery.

Instead of using the "neutral wire," you'll need to connect the positive wire from the trailer adapter to the positive terminal of the battery, and the negative wire from the trailer adapter to the negative terminal of the battery. This will allow the battery to charge while the trailer is connected to a power source.

It's important to choose a battery that is appropriate for your needs and is designed for deep cycle use. You'll also need to make sure that the wiring between the battery and the lights is appropriately sized to handle the voltage and amperage of your system.

Overall, while it's possible to connect the battery directly to the trailer adapter, using a charge controller can help ensure safe and efficient charging and protect your battery and other electrical components.

I mistakenly referred to the "neutral wire" when I should have referred to the negative wire. The negative wire serves as the "return path" for the electrical circuit and completes the circuit back to the battery, rather than a "neutral wire" as found in AC systems

If you're planning to use a battery to power the lights in your horse trailer, it's generally a good idea to use a charge controller to ensure that the battery is charged safely and efficiently. A charge controller helps regulate the charging process, which can help prevent damage to the battery and extend its lifespan.

In your case, it sounds like you'll be charging the battery using the AUX and neutral wires off the trailer adapter. Depending on the voltage and amperage of these wires, you may need to use a charge controller that is compatible with the input voltage and amperage of your power source. Additionally, make sure to choose a charge controller with the appropriate charging capacity for your battery to prevent overcharging or undercharging.

Another consideration is the size and type of battery you'll be using. Make sure to choose a battery that is appropriate for your needs, and that it is designed for deep cycle use (rather than a car battery, which is not recommended for this purpose). You'll also need to make sure that the wiring between the battery and the lights is appropriately sized to handle the voltage and amperage of your system.

Overall, while it's possible to connect the battery directly to the AUX and neutral wires, using a charge controller can help ensure safe and efficient charging, and can help protect your battery and other electrical components.