IMO I would not go with gray. It's an overdone color and doesn't have the character for the homes of today. I would go with a natural color, since you are in the woods - possibly an earthy warm green or a warm brown. To deal with the lack of symmetry, paint the house the same color as the roof. To de emphasize the utility/storage room door, I would paint it the same color as the house. Emphasize the main door with lighting, extra molding, and a modern wreath.

I would paint the storage door the same as the house color and add a nice sign that says "Skis" or similar to indicate it's storage. Paint the entry door a contrasting color. I agree to paint the house a natural color from the woods. We used to live in that area and had a cedar sided home that we stained a color called "Old Spar." It was about the same color as the trunks of the spruce trees in our woods, kind of a gray brown. I loved it and how natural it looked. There are so many wonderful greens, too. Almost any will work with the greens in the forest.
I wouldn't worry about the asymmetry. It looks like the area on the lower wall is blank to allow for snow accumulation. When you get some deep winter snow, it will look fine!
eta: you could also think about a lean-to type roof/room on that side of the house, either enclosed for extra storage or open for covered outdoor patio type area...

i agree with most comments especially on how to treat the doors. Imagine looking at the picture you showed us & the ski door is same color as house - it’s gone! I like your idea of adding lighting to entry especially around the front door not storage door. If you want to add interest to that side wall with no symmetry maybe think about adding a locally interesting wall ornament that’s weather proof. Iron art? Snowboarder? Per @Olychick comments,be sure to hang it above the snow line!

I like the color of the house as is. That would be quite cheery in a snowy landscape.

For the landscape. Define the parking and driveway space with a strong (stone?) edging to separate it from the planted areas. For the street side wall plant an understory tree or large open shrub with the intent of it being the focal point for a path on that side of the house.

Cute cabin. I agree with most of the suggestions above. Paint it a color of the woods. If you like gray, then paint It gray. Gray is used often in nature. Just don't use a dark charcoal gray. Nature gray is softer. As far as any kind of landscape, keep it natural and simple. Use native plantings. Nature is not symmetrical. And you don't want to spend your time at the cabin doing landscaping work instead of enjoying it.

Is the roof copper? If so, I suggest Crisp Romaine. Agree with painting the utility door to match the siding and the addition of lights (more copper?) and some stone to make a walk and planter beds that circle from the porch around to a covered deck with an open gable over it that repeats the angle of the windows above it or of the roof. That would fill the big blank wall, and perhaps a firepit a few steps away from it would be a nice feature.

Crisp Romaine 686 Paint · More Info

Thank you all for your suggestions! I will definitely look into some green and brown paint inspiration. Please keep the suggestions coming!

I would paint utility door the same color as body.

or

I love the colors James T. Farmer used on his house, Farmdale Cottage. It is brown, but not an unrelieved brown. His roof seems to be similar in color to yours.

While most of his colors are custom mixed, he lists these as very close:

Trim, columns and railing, BM Linen White

Body, Valspar Dark Chocolate

Door, Valspar Copper Canyon

Shutters, SW Zeus

This is a photo of the door that is painted Cooper Canyon.

I agree with Elaine’s color suggestions. Dark gray isn’t appropriate for the locale or climate IMO.

Gray in those woods would be dreary. Generally, the solution to an odd wall is a tall shrub, short tree. You probably won't find much that will grow under those hemlocks? Of course, if the wolly adelgid is as bad there as it is here, you'll lose tgem in 10 years.