Without wishing to pooh-pooh your normally sensible idea to explore during your stopover, might I suggest that the airport will be full of folk going on holiday for Christmas. This has many possible repercussions:
* Checking in again/queueing for security will take a heck of a lot longer than usual
* Local transport will be full and perhaps less punctual than usual
* As Judith points out, many of the shops and monuments will be closed
* You may not be able to go back Landside if you are officially 'in transit'.
* Flight times may be subject to change at short notice because of the
number of flights departing in a limited time slot
I would suggest that you accept your waiting time with patience and prepare for it with some Euros in your pocket to buy a meal, (or bring something special from home like sushi or turkey and stuffing sandwiches, mince pies, yummy chocs etc) and a good book or a 'travel version game' such as Scrabble or Monopoly to while away your time, and dream of all that sunshine and warmth ahead of you!
Have a great Christmas!