I don't see why a traditional decorating style can't be clean and clutter free. Personally, my taste leans more towards a clean-lines modern look, but if you like the look of your antiques and old-style furniture, why not make your goal to simply clear away anything that gets in the way of the visual look that YOU want?
If you have a lot of antiques, consider rotating them, perhaps on a seasonal basis. Displaying a few nice pieces with plenty of room to "breathe" will surely show them off to better advantage than cramming every inch of a cabinet, shelf, or tabletop, and will still reflect your chosen style.
By the way, although I do find minimalist styles inspiring, I think most magazine images take them to extremes that I, at least, would find undesirable to live with. How many real people wear clothing the way runway models do? That's how I see it. ;-) Be inspired by artistic presentations, but adapt them to your own real life.