I would suggest a light gray so it doesn't blend into the wall.

I wouldn't paint it dark, either. What are the colors in the room? I personally would prefer a green that connects to the patio or deck outside.

I would go bold -- orange or green

Your wall is now the focal point! If you add a "visual punch" or God forbid orange (seriously?) then the door will clash with all the natural wood tones. Strip it down to the natural wood finish on the inside, apply some paste wax or other natural finish and leave it alone.

A mid range blue (see below) ...as long as it suited your room's colors and I would paint both the inside and outside the same color.

I would match the bright green of the plants you see outside, lovely rustic wall!

I'm so glad I have the Houzz brain trust to help! Bonus points for aiding on the holiday. Inside is a fairly basic white, to let the wood wall be the star. You're all absolutely right about not going dark, I see now. I love all your suggestions and will start comparing them & looking at shades.

i've seen this done really beautifully (and playfully) with a canary yellow or eggshell blue or even a deeper teal/blue

there's no reason to put down other's suggestions... Do you want it to be a bold colour? It does depend on the rest of the room, but I think a lighter green or steel grey-blue might work.

or maybe leave it white

Agreed. I could see a bold, but this room also has a gray couch and a steel beam, so light gray or blueish may be just the ticket... though yellows or greens etc aren't out of the question. So excited! Beverly, I'm going to look up the name of that shade. It's pretty!

Here's a great use of red with reclaimed wood.

Just an update: Went with a light grey. For now, lol. Thanks again, all!