Are there any benefits to chilling the nitrous bottle?

No. Chilling the bottle lowers the pressure dramatically and will also lower the flow rate of the nitrous causing a fuel rich condition and reducing power. On cold evenings you might run on the rich side. For optimal running conditions, keep bottle pressure at approximately 900-950 psi, nitrous pressure guage that allows you to monitor this. If you live or operate a nitrous system in colder temperatures, it may also be a good idea to purchase a bottle heater kit, part #14164. Generally, ambient temperatures of 80-90 degrees Fahrenheit will allow for best power potential of nitrous kits.