The wainscot, the draperies, the chandelier and the furnishing you have don't really evoke "cozy" to me. The ensemble instead say's "traditional" to "transitional". IMO cozy is evoked more by darker colors, by more pattern and more texture.

Embrace your look: cool, momochromatic, sophisticated. Perhaps a couple of pieces of art instead of the mirror that could include some warm to es.

Replace mirror with art or a gallery wall. Opt for one large, warm-toned painting (landscape, abstract with earth tones, or a still life), or a gallery of smaller framed pieces to create interest and warmth.
Tapestry or woven wall hanging. These add texture and softness without being visually heavy.

Not shown in your photo is the rest of the room to the right of the mirror.

Is a wallpaper mural on the mirror wall an option? The photo below is the concept. I didn't look for a mural that compliments your existing furnishings.

I suggest a gallery wall to replace the mirror. You can also find wireless picture light sconces to place above for an added impact.

I would start by replacing the light fixture, nothing cozy about crystal chandelier.

maybe not exactly this, but something rectangular and textured.

The mirror wasn't a bad idea. The execution was poor.

IMO the chandelier was not a good choice for this room. I would have selected a fixture that is more linear in design.

Your room looks sooooo narrow. You can't change the size but that runner and linear candelabra is making it look slightly like a bowling alley. :) Remove both and put a warm wood bowl on the table.

Paint all the wainscoting the same color as your walls. The white line of wainscoting is bisecting this narrow space and making it feel so much more long and formal. Having everything one color will make it feel cozier.

Your drapes are great. But hang them all the way up at the ceiling and extend them all they into the corners instead of a few inches out. This will add instant coziness.

Do you love your chandelier? I like an eclectic look but this is feeling out of place. I'd go for a nice round orb light instead. Again, stay away from linear lighting here.

What you have currently seems to work pretty well. However you might look at doing artwork where the mirror is and doing some thicker window treatments. Please note the dining room designs we've included below with ideas for rugs, chandeliers, artwork, and window treatments.

Gem in the City · More Info

Gem in the City · More Info

Florida Coastal Retreat · More Info

Love the mural idea as well as removing the runner and candelabra - pretty room

To bring a warmer and more inviting feel to the dining room, I suggest replacing the wall mirror with a round art piece to soften the space and add character. Swapping the crystal chandelier for a black metal fixture that complements the candleholders will give the room a cozy, well-balanced look while tying the design elements together naturally.

A thicker or more textured rug and bulkier decor on the accent cabinet and a bulkier chandelier (perhaps a more rectangular shape that covers mire xeiling area) would help make the space more inviting.

We have similar style sense and I too struggle with msking my spaces feel cozy.

For me, a cozy room means warm, welcoming, relaxed, and intriguingly reflective of the friends who live there. Here's one take on that: