First check the obvious things like bad grounding wires/cables. If these are OK then likely the brushes in the alternator are worn out or the diode pack is shot. The regulator cannot freeze. On most models the Brush assembly and diode pack are integrated into one module held in place by two screws on the rear of the alternator. Once accessed it is easy (and relatively cheap) to replace.

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1991 M-B 560SEL Arctic White/Grey 99,000 Miles
1987 M-B 300SDL Ivory/Palomino 229,000 Miles (sold but never forgotten)
2006 Volvo XC70 Blue/Beige
1999 Porsche Boxster Arena Red/Savanna Beige
1986 Porsche 928S Goldweiss/Brown