Aven Trailblazer

• WWizards of the Coast2009-02-01
  Official Ruling
  Aven Trailblazer's second ability is a "characteristic-defining ability." It applies at all times in all zones.
• WWizards of the Coast2021-06-18
  Official Ruling
  The basic land types are Plains, Island, Swamp, Mountain, and Forest. Land types other than basic land types (such as Desert) don't contribute to domain abilities.
• WWizards of the Coast2021-06-18
  Official Ruling
  Domain abilities count the number of basic land types among lands you control, not how many lands you control or how many of any type.

Rulings via Scryfall