By 'heavy snow' how much are you talking about?
Do you have a plow, blower, bucket, or some combination of those?
It's kind of a judgement call. Around here, if it's snowing heavy, I try and let no more than a foot accumulate before plowing. I don't have a blower. If it's windy, though, there's almost no point in plowing because the wind drifts the driveway shut again and it just makes it worse if the snow drifts from the piled up side.
If you have a blower, then you don't have the problem of making piles of snow along the drive to get drifted over higher than what you started with.
Ice is a different critter. As others have said, and you appear concerned about, if you clear the snow down to the ground, then ice falls, you'll have a skating rink until you salt it, or the sun shines, or temps warm up, or more snow falls on top of it.
I'd probably leave a few inches of snow hoping the ice would fall on top of it, then when it stops, remove it all at once.
But if it snows, then rains and turns the snow into frozen mush, you're gonna have that to deal with.
Again, it's all a judgement call based on your gut, experiences and local weather forecast accuracy. Good luck. Let's hope the forecasters get it wrong and it stays snow or rain.
