Absolutely right, follow the max cold pressure on the sidewall of the tire.
Don't trust a sticker on the side of the trailer, it doesn't have any idea what tires you have or what operating pressure they were designed to use.
If you are running >50 psi, make sure your valve stems are either metal or have a metal tube (inside the rubber stem). If they are all rubber, they are likely standard stems, only good for 50-60 psi. VERY COMMON error, even by tire shops ;) They can bleed down over time, leading to possible catastrophic tire failure.