Stone pillar in conservatory damp

I think if you now google for the largest possible thermal bridge, your picture will come up. That is really intense. Has the winter garden been there for a while? Either insulate from the outside or just wipe it down daily.

Presumably, only external insulation is possible, and the whole thing should then be integrated visually in a sensible way. Either a trellis in front to hide it or the opposite with some decorative elements (e.g., bossage stones) to visually highlight the whole so that it looks as if it is supposed to be that way.

if it is only damp now, at -10 degrees outside you will have frost flowers inside.
felt inside 10cm wide area and outside 50cm, how is the small area supposed to warm the column,
outside insulation or column renewed with thermal armor

I would also clearly recommend insulating from the outside, if necessary you could upload a picture of the exterior view. Then it might be possible to gather ideas on how to implement the whole thing. Otherwise, it will hardly be possible to tackle the problem.

For me, the whole thing in its current design is a flawed construction. Heating the column from the inside is also just treating the symptoms. For me, only insulating from the outside would be an option!

Are the window sills actually continuous as well and therefore thermal bridges?

Have you possibly already had a conservatory builder there, to see if a replacement of the column might still be possible afterwards?