A few things to consider on the resurgence of magic
The White Walkers haven’t been seen in the South in 8,000 years. The Wall and the Night’s Watch have successfully kept them at bay, long enough that they’ve passed into legend for most Southrons. But the White Walkers probably never died out and came back. Craster’s been dealing with them for some time prior to the start of the show.
However, the rise of the White Walkers is the first fantastic element in both the books and the show - the opening scene in the show of the Men of the Night’s Watch being killed by the White Walker and the Wight girl is also the prologue in the book.
Also, Mance Rayder has been gathering his army and leading them south for some time. So the Wildlings are already fleeing the army of the dead when the story begins.
The Targeryans conquered Westeros some 300 years before the story begins, so healthy dragons were still a thing then. It’s been around 100 years since the last dragon died, and the last few weren’t as strong as their predecessors. It’s around this point that magic begins to decline as well.
In the interim magic still works, but definitely not as well South of the Wall as it does North. The Three-Eyed Raven is able use his greenseeing abilities, for example, and Warging remains an ability some Wildlings can use. The Pyromancers can still make wildfire, but it loses potency. In Qarth the Warlocks can still use their magic, but it’s harder to do things. We don’t know if Mellisandre can cast the glamour spell that makes her look young at this point, but she is incredibly long-lived with no lost of mental faculties.
Given the timeframes involved with the story, we can assume that magic is resurgent before the end of series 1/A Game of Thrones. Mellisandre is ensconced at Dragonstone at the start of series 2/A Clash of Kings, and nobody noticed her changing to a younger woman, so she was able to cast glamours before she arrived there. In the books, rumours of Robb warging into Grey Wind begin before he’s declared King in the North, though he’s the only Stark child that we don’t know for sure that he was actually a warg (in the books, Jon, Arya and Bran are, Sansa isn’t)
The things that are unclear are:
Did magic decline at all North of the Wall?
What have the White Walkers been up to for six thousand years?
Is there any correlation between the resurgence in magic and the comet or the birth of the dragons?