雨 and 雪: falling precipitation and what remains
Distinguish what is falling now from water or snow left afterward.
Sentences about rain
雨 (あめ) means rain. 「雨が降っています」 says it is raining now.
「雨がやみました」 says the rain stopped. It does not establish that the ground has completely dried.
Snow and remaining cover
雪 (ゆき) means snow. 「雪が降り始めました」 says snow has started falling.
「道に雪が残っています」 says snow remains on the road. It does not establish that snow is still falling.
Forecast versus observation
「明日は雨か雪の予報です」 forecasts rain or snow tomorrow. It does not report precipitation that has already occurred.
「雨から雪に変わりました」 says rain changed to snow. から and に identify the earlier and later states.
Does 「道に雪が残っています」 mean it is snowing now?
Show the answer and why
No. It describes remaining snow; current snowfall is separate information.