I just spent a few minutes (didn't take long) comparing the eight magical traditions in 5E with the various spell schools in 1E, and how in Dragonlance, your wizard's robe color determines which spell schools you can know/cast. And it turns out they easily map together, giving five of 5E's eight groups to each robe color. Also, the influence of the three moons seems like it will be pretty simple to apply to 5E's Wizard class.
Class: Wizard of High Sorcery
Except as noted below, identical to the basic Wizard class.
2nd Level: Arcane Tradition
Wizards of High Sorcery have limits on which arcane traditions they can choose from, based on their alignment. Wizards of Good alignment can select from Abjuration, Conjuration, Divination, Enchantment, and Evocation. Wizards of Neutral alignment can select from Conjuration, Divination, Evocation, Illusion, and Transmutation. Wizards of Evil alignment can select from Conjuration, Divination, Enchantment, Illusion, and Necromancy. [Note that the Law/Chaos axis does not matter for this choice, only the Good/Evil axis.]
3rd Level: Robes
After achieving 3rd level and before gaining 4th level, the wizard must pass the Test of High Sorcery, which is pass or die. The wizard who passes joins one of three orders, White (good), Red (neutral) or Black (evil) and is issued appropriately colored robes. From this point forward, they may only cast spells of the spell schools allowed as valid choices for their Arcane Tradition. Spells of prohibited schools in their spellbook are unusable, and the wizard may select any one such spell, if any, to be removed and replaced with another spell by the Conclave of Wizards upon completion of the Test.
After passing the Test of High Sorcery, the wizard's magic is influenced by one of Krynn's three moons: Solinari (White), Lunitari (Red) or Nuitari (Black). When the wizard's influencing moon is in High Sanction (full), the wizard gains a +1 bonus to their Spell Save DC and Spell Attack Bonus. They also gain one additional spell slot that they can cast, of the highest level of which they can cast 2 or more spells. When the influencing moon is in Low Sanction (new), the wizard suffers a -1 penalty to their Spell Save DC and Spell Attack Bonus. They also lose one spell slot of the highest level of which they can cast 2 or more spells.
For example, at 7th level, a Wizard has 1 4th level spell slot and 3 3rd level spell slots. At High Sanction, the Wizard would gain an extra 3rd level spell slot, for a total of 4. During Low Sanction, the Wizard would have only 2 3rd level spell slots. Once the Wizard advances to 8th level and has 2 4th level spell slots, the Wizard would have 3 4th level slots at High Sanction and only 1 4th level slot at Low Sanction.
Renegade Magic Users
A Wizard who continues to advance in level beyond 3rd without having taken the Test of High Sorcery is considered a renegade. The renegade may cast spells of any spell school regardless of alignment, and the moons have no influence on the renegade's spells. Any Wizard of High Sorcery who encounters a renegade is bound by the Conclave of Wizards to attempt to capture or kill the renegade.