polyline creation - How to derive vehicle paths from timestamped location data?

I've got a bunch of location data for snow plows. There's a unique id for every plow, a timestamp, and x & y coordinates.

Instead of knowing where hundreds street plows were at one minute intervals, I'd like to know which streets have been plowed.

I know there are ways of turning points to polylines, but does anybody know of a method to snap the points to the street grid? In other words, of deriving vehicle paths that hug the streets?

The reason I think that turning points to polylines probably isn't enough is because I only have location data for every plow every 60 seconds. This means there aren't coordinate points for when plows were turning at certain intersection, so if you just drew lines between points some of them would cut through blocks.