Enemy Level
Enemies found in the "Icecrown" zone range between level 77 and level 80. Most of them are normal, although some elite enemies will appear in certain locations or as part of a quest. Depending on your character's gear and on your playing skill, you may be able to kill level 77 enemies as early as level 74, and level 80 enemies as early as level 76. Being able to kill higher-level enemies can be useful if you are gathering ore or herbs in Icecrown. However, attempting to grind experience by killing enemies in Icecrown while at a lower level is most likely going to be less efficient than completing quests in a more level-appropriate zone, unless you can maintain a very high killing speed.
Quest Level
All quests in the "Icecrown" zone require your character to be at least level 77 to be able to accept them, without any exception. This includes regular questing progression within the "Icecrown" zone, as well as all quests related to the "Argent Tournament" event, found in the northeast corner of the zone. If you are trying to level efficiently, you may find it beneficial to switch to questing in Icecrown as soon as you reach level 77, as the quests will grant more experience than the easier quests you may find in a lower-level zone.
Similar Zones
The only other zone that matches Icecrown in both enemy and quest level is the "Storm Peaks" zone. Which zone you choose to level in largely depends on your personal preference. Icecrown has lengthy quest chains steeped in "Warcraft" lore and the events that led Arthas Menethil to becoming the Lich King. "Storm Peak" quests, on the other hand, serve as an introduction to the story of the titanic watchers created to serve as the guardians of Ulduar and the events that led to their betrayal by one of their own.
Considerations
Due to the lowering of experience required for each level that occurred shortly before the launch of the "Cataclysm" expansion, most players are able to reach level 80 and move on to "Cataclysm" zones without ever entering Icecrown. Many of the quests in Icecrown require a group to complete; if you are playing alone, you may have issues finding a group for these quests due to the lack of players in the zone. If this happens, the only solution is to ask your friends to help or switch to questing in Storm Peaks, a zone with a far lower amount of group quests.