Hey mate, can't offer much insight at the moment regarding a fix, but the 525i touring i just got has the same cold start cough and splutter and the idle issue. Although mine is an M50, i can't imagine there would be much difference. The icv could be a good starting point for me, or the other possibility is an air leak, my Audi one, plugged it and no more cold idle issue... It's just a case of finding it...
1989 BMW 318i two door Schwarz - Boris
1988 BMW 318i two door Lachssilber - Bruno
1996 Audi A4 1.8T Aluminium Silver - No name, it has no soul.
1992 BMW 525iT - Cashmere Beige - Barry Bimmalow