I grew up in Lowville, about 40 minutes south of Watertown. I also lived on Ft. Drum when dh was in the Army, lived in Watertown for college and lived in/attended college in Potsdam. If I had to move back to the region tomorrow (to a town besides Lowville or Croghan), and wanted a reasonable commute from Watertown, I would live in Clayton. Clayton is a small town on the Saint Lawrence River. It is walkable, cute and friendly. You can hop onto the river any day you like and still be close enough to work to not hate the drive home during a blizzard.
You can start expecting snow in Nov.-Dec. though we always seem to have stickable snow by Christmas. Just count on solid snow until April. Regular snowfalls are 1-6 inches. Larger snowfalls are 7-12 and big storms are measured in feet. It does get very, very cold. Wind chills will drop things down in the -30's on the very worst days. The best thing to do it to engage in winter activities such as skiing and snowmobiling. That way you look forward to winter.
As you've seen by now, Watertown has a central strip where you will find chain eatery's, the mall and box stores. If you want a larger mall, you can head to Syracuse.
I am a huge fan of the whole region. I am living in the Capital region of NY right now and I look forward to my eventual return to NNY.