Those windows are So Beautiful! I would Not do a thing.

thanks for the comment, I was thinking may be just a delicate pelmet and leave it at that?

+1. Stunning home and setting.

A pelmut would be on the woodwork. I would do a roman shade inset mounted so it only hides a little glass

Too beautiful to obstruct the view and any covering would take away from the room IMO. Very pretty room!

No curtains beautiful windows with beautiful views

Wow...are you sure a question like that doesn't require a site visit? Seriously, if you don't need coverings for practical reasons, don't bother as the room is beautiful.

if those are single glazing, you might wish to have roller blinds fitted against the window and hidden by trim work painted to match the window trim. You would lose a few inches at the top but a talented trim carpenter could make them look almost like a part of the window trim.

I could see custom made radiator covers that would mimic the wainscoting would turn those obstructions into a desirable feature. For the top use the same profile and dimensions, at the same height, as the window sills. Columns on the ends and probably three panels of approximately same proportions as the existing ones across the front of the radiators would work well. Do some research on radiator cover design as you need to have good air flow coming in from the bottom and exiting at the top and a properly designed cover will actually help, not hinder heat distribution from the radiators. Despite the term, more heat comes from convection than radiation and channeled air flow will increase the heat transferred to the room.

Let me know if you need a link to info about radiator cover designs