Lise Meloche (world cup gold medalist). Source: Wikimedia Commons
Here are 3 snow-covered areas that are great for nordic skiing.
The frozen reservoir of Brno dam
The artificial lake in Bystrc is covered with snow and many people use the huge area for skiing.
The greates advantage is that there are many pubs where you can drink hot tea or grog.
Map
Forrests around Kohoutovice
You can enjoy really fresh air in the woods covering quarter Kohoutovice, located high above the town. Contrary to the flat reservoir, prepare for challenging tracks going uphill and downhill.
Map
Hády
This is where I was skiing with my parents when I was a kid. Hády (or Velká Klajdovka) is a large forrest located next to quarter Líšeň. It offers dozens kilometers of nice cross-country skiing tracks.