My guess would be that all arcane classes would fall under the rubric of the Orders of High Sorcery, with the Test coming at the end of Heroic tier, and a separate paragon path for each of the White, Red, and Black Robes.
That's assuming the Orders and the Test still exist, of course.
They do. In AD&D, the Test happened between 3rd and 4th level. In 3.5, the Test typically happened at 4th level, with your 5th level being when you could take the Wizard of High Sorcery prestige class.
You could apply the 3.5 scenario to 4th edition with paragon paths, but that's an awfully long time to wait to be able to play a WoHS. Some games never even reach paragon levels. It would stand to reason, then, that the Test be taken at lower levels, gaining access to the ranks of the WoHS. Then the paragon paths could be reserved for specialty roles, such as renegade hunters or the Kingfishers.
In fact, I think organizations in DL will likely be separated from paragon paths, save for specialized roles.
Now, as for the arcane classes and the WoHS, I'm afraid I'll have to disagree slightly. In SAGA, they introduced sorcery and mysticism, which were essentially "replacement magic" for arcane and divine magic, respectfully. After the War of Souls, Dragonlance found itself with four types of magic - 2 arcane and 2 divine.
What that means, is that in 3.5, the sorcerer wasn't drawing from the arcane magic of the moons. He drew his power from the ambient arcane magic of the world itself. Unless continuity is thrown out, then the sorcerer would exist outside of the WoHS. This adds a nifty dynamic and conflict.
Warlocks, then, would be problematic since they make pacts. Now, if you had one pact per moon god, they would work out fine.
As for swordmages..."A warrior has his sword. A wizard has his magic." They really don't fit the theme of the Orders. I could see them being practitioners of the same wild sorcery that sorcerers use.
Artificers and bards also work out in Dragonlance, though in both cases, I would also go with wild sorcery. One of the SAGA schools of sorcery dealt with the same sort of stuff that artificers deal with, and bards in the WoHS just seems weird.
So yeah, all the arcane classes can work in Dragonlance, the warlock requiring the most work. There may need to be some tweaking, but that's the case with any world. With the existing setup on magic, there can be some nifty dynamics.
That being said, if there is a total reboot, then it may be best to lump everything together under the WoHS. *shrugs*