Your furniture is a very classic color so it should work with almost anything. I would begin with color. Maybe choose some bedding in warmer colors, then add a colorful rug, curtains, and then appropriate art.

Your bedroom is already neutral. Everything in it, including the furniture, is a neutral. To make it softer, cozier, and happier, you will need to consider changes to bedding, draperies, and paint in addition to the rug and lamps. The room doesn't seem cozy because it is not personalized to you. Almost any non-neutral color will go well with the furniture and floor.

Find a bedding set or a rug that you love and let that be your starting point. Everything else can flow from that.

What colors would you like to see in the room? Do you like warmer reds, oranges, or yellows or do you prefer cooler blues and greens? Either could work with your warm toned furniture. IMO, the first step is to find a rug with some color and pattern and then go from there to choose lamps, pillows, and artwork. As it is now, the room is void of personality. You need to put a little of YOU in there to bring it to life and make it feel warmer and more welcoming.

As a home stager, we often use white to soften a room with dark furniture and it can work for your situation as well. A few ideas, a white comforter/duvet: https://amzn.to/32saWOc 

pair it with white sheets and pillowcases and have throw/accent pillows in your favorite colors to have 'pops' of color. On the nightstands, have lamps with a beige or taupe base and pair them with white lampshades. At Home has great area rugs to complement the room. That will get you headed in a good direction and the furniture is really nice. #affiliatelink

I don't think a neutral scheme works very well with very dark furniture. Embrace it. Add lots of color. Start with a colorful, traditional rug, then pick up the accent colors for paint and bedding.

A few inspo pix:

Traditional Bedroom · More Info

Clear Creek · More Info

That wood is a gorgeous colour and already exudes warmth. It just seems that there isn't any harmony between the furnishings and furniture colour, and there's also a very stark contrast between the dark brown and pale ivory/white of the furnishings. Essentially the room is almost finished but needs a few pieces to soften it and blend it together.

Perhaps try pieces to integrate the colours together? I would suggest perhaps a duvet cover in cream/deep ivory shades, and some decorative scatter cushions with ivory and another colour. You also have a blue cushion, which is a nice cool colour to bring in. Perhaps integrate that into the colour scheme. For example a blue and ivory/cream scatter cushion with a blue runner on the end. Try also painting the wall behind the bed, or simply hang art above the bed integrating the blue/brown/beige colour scheme. Try a blue runner and a faux sheepskin draped across the end of the bed.

I've put a few example pictures. The warmth and softness comes from using finishing touches, like the runner and layers on the bed, rug beneath the bed etc. A piece of art will finish the room off nicely. Let us know how you get on with some photos!

Do you sew? You could make a slipcover for your headboard. This link shows how. Thistlekeylane.com

A few ideas:

Your furnishings are classic and look really good.

Like the lamps but if you replace them, consider tall thin with larger white shades.

White bedding always works but you could also choose several pastel colored pillow shams to chill the stark contrast between dark bed and light or white bedding.

You don't need a full room rug but a pair of runner rugs -- each side of the bed -- to coordinate with your pillow sham selections could be a good idea (especially in winter when mot floors are a bit cooler than room temperature).

You could paint one wall as an accent wall.

Not sure what you have at the foot of your bed but a real cedar chest -- lighter in color -- for your bed linens and use as a seat goes with any bedroom furniture because it has a specific nature an purpose.

You might consider adding tall narrow modern wall hung shelving on each side of your chest of drawers and, again, use a color that coordinates with your pillow sham and rug choices -- not dark like the furnishings but not as pale as the wall. If you choose a cedar chest, you could also choose cedar shelves.

https://www.ikea.com/us/en/p/lack-wall-shelf-unit-white-60282186/

Although "art" or mirrors above your nightstands or headboard might seem to be an obvious answer, consider coordinating whatever you choose for that wall with something else in the room you add on the wall across from it (beside/above tv and chest of drawers) and don't limit your consideration to traditional framed pictures.

You already have a blue pillow sham? There is blue in this:

https://www.touchofclass.com/evening-sunset-wall-sculpt/p/Y362-001/?kc=DMFPFS8&code=DMF03&color=&size=&tid=DMFPLA&gclid=EAIaIQobChMIrvaU9f7m6wIVCYbICh1Neg-hEAQYByABEgI7lPD_BwE