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.