How does the salt affect the plants growing alongside the road?

Answer 1

Salt can cause chemical injury to plants. But in winter time, most plants are dorment. Most salt goes down storm drainage. The remaining salt in soil is leached out by water from melted snow. Damage is usually minimum.

Answer 2

Well, salt tends to kill most vegetation. If I remember correctly, the Roman army used to sow the fields of enemies with it, in order to completely decimate their crops, and prevent future agriculture. Essentially destroying those lands and the lives of the people...
So unless there is an additive in salt now days used to keep streets ice free - I'd say it still either kills the plants, or severely harms them...

Check these sites out:
http://www.rittenhouse.ca/hortmag/glynis/salty.asp
http://counties.cce.cornell.edu/yates/4055.htm