With asphalt millings/RAP what the original source was maters. If they still have some AC(asphalt cement) content then they bind very well. If they are from a 40 year old road, full depth milled, then they really aren't likely to have a good AC content. Some millings have chunks that tear out, maybe 6" long X whatever the depth of mill is (1-3"); others are a nice gravel like texture.
We don't plow snow where I am so I can't comment about that part. But for drive ways you basically have a couple options
Concrete=$50/Sq yard and lasts well if done right
6" limerock=$4.50/Sq yard ($2.50 in rock ($6-$7.50/Ton), plus at least another $2 in trucking) washes badly if water has any speed to it
6" Millings/RAP=$5.50-$10/Sq yard (prices of millings range from $10/Ton to $20/ton around here) doesn't wash much, isn't dusty unless you really haul butt down it
6" rock and 1.5" Asphalt=$12.50-$25/Sq yard; asphalt isn't that expensive, it's just that there isn't any good small outfits (broad brush I know) and mobilization is at a bare minimum $500-$1500.
For any of these you should strip the grass. Generally if you are doing 6" of millings, you would cut out 6" of material so the rock or millings is "boxed". If you dump millings on grass, two problems: 1 grass grows through; 2 you have millings on the side that aren't contained where they belong.