Yes, take down wall but check to make sure it is not load bearing. A long Island with barstools would really open up the space and give you a lot more counter space.

I don't know much about this, but it seems the radiator might be an obstical in taking down the wall. What I can speak to however, is that in old homes totally taking down a wall can seem awkard. My parents ended up adding more wall to an opening to create an archway and you would be amazed at the difference. It made the space make sense, where it wasn't quite right before. I would go with a arch in the space to keep it true to the style. Bonus, if this is a load bearing wall, that means you would need to leave a header, which an arch would have anyway, so you can probably remove part of it no matter what.

Thanks, both posters! I like the idea of an arch. Maybe a squared arch, if that's a real thing, to keep the feel of the moldings. This is a load bearing wall and will need a steel beam. An arch helps solve that issue.
Soon I'll be asking about flooring. I look forward to your opinions!

Looks like you've got electrical to deal with too. Maybe you should imitate the front door and add a transom at the top. You'd have to seriously redo the kitchen for it to go with the green room. I don't see that it is a simple project.

Oh. To clarify, I'm only interested in knocking down the wall on the radiator side of the dining room.
One idea is to expand the doorway almost to the wall at right, which would echo the dining room's wide doorway into the living room (not pictured). The next question,then, is how to integrate the bar/counter and radiator enclosure with the edge of the door frame?
We're thinking white stone or marble counters in the kitchen with dark wood cabinetry. But should the wood on the dining room side be white? So awkward-seeming. Maybe we could flip the color scheme for this bar: white cabinet or legs with a dark live-edge wood countertop?