I think the optimal ages for visiting a big European Christmas Market are Baby (0-18m) and Child (7+).  I cannot imagine staying sane in the crush of humanity, lights, and sounds if I had to keep track of a toddler.

A baby in a backpack is a wonderful companion for a cold night in Marienplatz, Munich, though.  He happily spent all day staring at the people and ornaments, napping when he needed to, and sharing bratwurst and warm cider with us (OK, we might have tended towards the Gluhwine).  After night fell, he goggled at the billions of beautiful Christmas lights and was enraptured by the carolers, before passing out on a bench in the Rathskellar, while we enjoyed jaegerschnitzel and beer.  He had his first solid food on this trip to Germany (at a Thai restaurant, what?!) and has been a fan of German food since.

We all enjoyed this trip immensely - the only parental mistake was not putting the kid in long underwear.  Despite being otherwise bundled up, his pants would ride up and expose bare leg in the backpack, and every oma in the market would grab his chubby little legs and rub them while chiding us:  "Ist ganz rot!  Ist sehr kalt!"  A stroller would have been easier on our backs, but harder to maneuver in the crowded market and on the cobblestone streets, and in the backpack, Das Kind could see everything going on, not just adult legs.