I've often wondered when fishing in rivers/streams, do all fish constantly move downstream or do they move up and down the river but stay within a certain area?

Forgive me if I misunderstood your question but if smallmouth only moved downstream, wouldn't there be no fish in the river after they all moved downstream?

I think he meant to over winter. 

 

If so, that's more of a northern thing (like Canada.) Not sure about Indiana, but in my area they stay put for the most part and find areas with slack current, access to food, hard bottom, deeper water and easy access to shallower areas. Find good and steep vertical break lines in slow moving water and you'll probably find lethargic winter smallmouth. 

 

If you're talking in general terms, there are many studies that have been conducted with tagged fish. Smallmouth typically enjoy a wider range of movement within a body of water than largemouth, but both typically stay close to home. There are many exceptions that have been noted in tagging studies. Trout will often spend most of their lives within a very small area with the exception of the spawn. Muskies will often cruise miles of river. There's no definitive answer for any species, but there is a lot of information out there if you're interested.