'66 Stang 289 starter issues

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The past few times I tried starting my 66 Mustang(289,4speed), the starter was turning very slow as if I had low voltage in the battery. The battery tested fine. The last time I attempted to start it, it barely cranked and didn't start. I noticed some smoke coming from near the voltage regulator on the radiator support. It turned out to be a ground wire heating up to the point where it charred the insulation. This wire came out of the harness and was grounded to the top voltage regulator mounting bolt. Would a bad starter cause this wire to heat up? Two feet of snow in Rhode Island has prevented me from crawling under the car and removing the starter.