The only thing we can do for you, is recommend insulating techniques. It's up to you to select one that "looks good" to you. Or, possibly, "looks least bad", as slapping insulating material on a part of a window will likely look bad no matter how you approach it.
With the thought that anything applied to part of the window/frame may end up looking pretty shoddy, I would suggest looking at applying an insulating layer over all the "woodwork" of the window.
Take a piece of insulation (foam would be good, ensure that it's approved for use in your area - remember, some foams can give off toxic fumes should they be exposed to flame), cut it to the size of the window, then lay out all of the frame lines, sash, and mullion bars, etc, then cut out the openings where the actual glass go.
Now you have a duplicate of the window's "woodwork" made out of foam. Attach this with some double stick tape to the actual window frame. The "woodwork" is now deeper than it was, but it's still consistent across the entire window. If desired (and you have some skill), you could cut a profile into the foam to match the profile of the existing windows. (This site (first result of an internet search) shows some traditional (US) patterns to show what I'm talking about). You could approximate these in foam if you already have them, or you could spruce things up a bit by applying a profile where none existed before if you wanted.
It sounds like you have a 3-window unit, so you'd need to duplicate this process for all 3 windows at this location to keep the appearance consistent.
Since insulation foam (in the US, at least) is usually pink, blue, or green, and those colors probably don't go well with your decor, enhancing the "ugly" factor. Prior to installation, paint them (spray paint designed for plastics should do the trick) an appropriate color.