Update, I did some more work last night.
First I picked up a 1x2 which I attached with some wood glue and my nail gun.
For the exterior, I picked up a 7' piece of 1x6 red oak (I decided to splurge). I wanted to miter the oak and I'm terrible at making cuts, as you can probably see from my photos..., but I thought I would attempt it anyway. I decided that I would make the cuts and just flip the board over so they matched up. The front was made to exact length and the other two were made with a couple of extra inches off the back so I could just cut those straight. It worked perfectly.
I lined up the miters and just used wood glue and my nail gun again. I've seen other posts with people bolting the exterior. I just don't see the point. The wood and nails were solid and I wanted a clean finish to red oak. Plus the nail gun was just so much easier. I just made sure I didn't put any nails near where the shanks were going.
I've also seen people building the collar directly on the cooler but I just built it on a table and decided to trust my measurements.
I dry fitted the collar one more time and I was really happy with the fit. It is really snug which is the way I wanted it. I have to actually give it a good push down and its totally flush and doesn't budge.
You can see in the pic that the 3/4" from the 1x2 really made a difference on the hinges. I can now attach it with all the screws and not have to make any additional holes in the freezer or hinges.
I then took the collar off, chalked the gaps on the interior, and used wood filler on all the nail holes.
Good enough for the night. Time to kick back and have a homebrew!
Next step, cut shank holes, sand, stain, and poly.