If the mold is showing on the underside of the overhang of your roof, it is likely that the heat escaping from your house is melting it. You may need a deeper overhang. Your roofing material may also be failing at that point, causing a leak. Contact a licenced contractor or roofer for further information.
If by "inside the roof" you mean the underside of the plywood up in the attic or crawlspace, the issue of melting ice is still true and water is leaking into the home. Water is coming in and freezing causing the appearance of frost. The black is mold and will eventually destroy more than just your roof. Your family's health can be directly affected by the presence of mold in your home. Get a licensed contractor or certified roofer to inspect. Proper insulation and ventilation will keep your roof functioning for years. A few hundred dollars now in repairs will save thousands later if you have to replace the entire roof! If it is in one area, there is an air leak causing warm moist air to escape from the living area. commonly found over bath vent fans and ceiling fixture boxes. seal air flow with spray foam, not just insulation. if over large area then you need more roof ventilation. my experience shows "code" ventilation isn't enough.
The colour of the roof has a significant effect on the temperature inside a house unless there is a very large amount of ventilation in the roof space to disperse warm air, and a very high level of ceiling insulation. A dark roof will absorb much more heat than a light roof, and will conduct or radiate this heat into the roofspace and then into the house.
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