Size of Garage door

As stated, slope can make it insufficient height.

My door is 14’ high x 20’ wide and it works fine.

It has been several years since I built but Wayne Dalton made my door and opener. I believe it is commercial because of the size.

The height of the door can also come into play depending on the slope of the driveway. If the approach is a steep angle you will need more room at the door.

If the door is actually 14' x 14' that is a good size, my 5er is 13'4" and most states have a 13'6" maximum height (without a permit).

A rollup or accordian door can be any height, but they get pricy.
Understand that a 14' tall opening does not equal 14' of clear access.
The average overhead door when open will hang down anywhere from 6" to a foot or more below the top of the framed opening.
Your 14' door should be fine with a 12'6" trailer, but you must watch to ensure it is staying up as far as possible.
You may even want to cut a piece of tubing such as the lightweight tubing used for a tv antenna mount to something like 13'6"" and use that to ensure the bottom of the door is always above your highest point before backing in.