Yes you should inflate your trailer tires to the max recommended PSI air pressure especially when the weather is cold.
If your tires are underinflated then it can cause the tires to overheat and cause a tire blowout so make sure the tires are properly inflated.
Underinflated tires even in the summertime can overheat and cause a tire blowout so always check your air pressure in your vehicle tires and trailer tires before you head out especially on a long road trip.
I always check my tires air pressure on both my car and trailer when I'm on a long road trip after 2 to 4 hours of driving just to be sure I haven't lost any air pressure.