I believe (and I have ready tagging studies to back it up) that stripers do migrate. They are not all just nearby and happen to magically show up when the temperatures get warm. There are two major breeding stocks, the Hudson stock and Chesapeake stock. All breeding fish return to their spawning ground every spring to spawn from what I understand. Also, to explain why the fish seem to magically show up all over around the same time you have to believe (I have read this somewhere) that the Hudson and Chesapeake bass take different migration routes. From what I have read, the Chesapeake fish make their northerly migration around Montauk, while the Hudson fish come up the east river and follow the river herring along the CT shoreline. I have also read the the Hudson fish don't migrate as far north as the Chesapeake fish. I have also read that regardless of where the fish were spawned, all the cows (I am talking 40"+ fish) winter over down south. Not all stripers migrate, and not all stripers migrate north. Some Hudson fish migrate south to Jersey, and some don't migrate at all. I have also read that LIS is actually considered part of the Hudson estuary, and as a result small bass are caught in LIS that are mistaken for locally bred fish, when in fact they are Hudson River fish. The smaller bass will move from upstream and spend the summer not straying too far from the river. Then there are the winter over contingents. These fish are all Hudson River stock fish that for whatever reason, spend the winter somewhere else. They don't spawn where they winter over if they are of spawning size, they return to the Hudson. While it is nice wishful thinking that bass are spawining locally, I have talked to several biologists that say that the rivers and streams in CT simply don't have the environment to support successful spawning.
As far as the wintertime goes, I believe that salinity and the size of the fish make a difference. If I remember correctly, stripers have trouble breathing in fresh water at cold temperatures, and it depends on the size as well. Tidal rivers that have winter over populations need a salt water wedge and deep holes for the fish to hold in. When the water temps are very low, the fish will stay deep in the salt water and not move much. The halocline is a glass ceiling above which the bass don't move. "Over'Winter Striper Secrets" by Al Anderson has a good discussion on migration, winter habits, and results of tagging studies. I read the book a number of years ago so I can't guarantee that I'm getting all the details 100% correct.