Take a look at
Gothic 3(or even the whole series; although I've only played #3 so far so can only comment on it).
Like some of the other recommendations, it doesn't meet every one of your criteria, but it meets several.
Yes - Open world (large and seamlessly open - no loading zones anyplace, including going into towns and dungeons [both large and small])
Yes - character customization
Yes - fantasy setting
No - mounts!!!
Yes - loot (excellent loot system; is very rewarding to "explorers")
No - possibly a class with pets, like the warlock in WoW (BUT - you can turn into various animals, depending..)
Yes - third person view preferably, not isometric
Yes - I would prefer an action-oriented combat system, but one similar to WoW is fine. I would prefer not being a turn-based system (It isn't turn-based)
The world consists of 3 "biomes" (Temperant with mountains, plains, valleys), High mountains (snowy and icy; one of my favorite areas in any open-world game - it's so well done IMO), and Desert (hot and dry). All of the areas have ocean borders (yes you can swim; and there are places to swim to); and transiting from one biome to another is "seamless" (you just make your way between them; either overland on-foot or via the fast-travel system).
Exploring is rewarding in that there are tons of hidden nooks and crannies - usually with stuff to loot - including some really good loot. So climb those peaks and check behind those boulders <g>.
There are multiple "factions"; and you can earn friendship with them or turn against them.
Etc., etc.
It's a great open-world game IMO.