Plywood is not "routable" is it (ie I could not rout some of the existing ring down to make room for a seal?
Yes, it is.
It would be easier though, to use a flush trim bit to remove the protruding material, as Steve suggested to give yourself a spacer.
By adding another ring on top of what you have, you will have provided a space for a quality weather seal.
Plus, if the seal is placed on the trim ring where the door buts up to it, water can still get in the gap and channel down the gap to the bottom. It may not can get in the trailer, but would still impact the wood door at bottom as it is doing now
Two issues here;
The first is that the wood must be
completely sealed against water, not just a little, but completely!
If it is not, your trailer will self destruct, usually faster than you may imagine, and it won't happen a little at a time, giving you an opportunity to correct it, but rather suddenly you'll discover that the damage has been done and it is too late...
(It actually does happen slowly, but it will be hidden until it is too late).
The second is that water will always find a way into any crack or groove (your door in the door frame).
Accept that it will happen, and you can focus on ways to temporarily block (weather strip) and divert (gravity) the water, be it from a gentle spring shower, or 70 mph driven rain.
The bottom of your door opening, the horizontal trailer body section, will benefit from being beveled.
With weather seal in place, the water will get in the gaps, meet the weather seal, and travel to the bottom, where the bevel will direct it away from the gap, down to the ground.
Once you are sure all that is good, adding a gutter or diverter will help a little, mostly to keep morning dew pooled above the door from dripping on you when you are getting out of the trailer.
It won't/can't replace proper design and weather sealing.
I can't find a good shot of the bevel on the wood at the bottom of the door opening, but here is one of the diverter over the door.
Rob

Waiting for "someday" will leave you on your deathbed wondering why you didn't just rearrange your priorities and enjoy the time you had, instead of waiting for a "better" time to come along...