In the annals of the Further East, it was the Blood Betrayal, as his usurpation is named, that ushered in the age of darkness called the Long Night. Despairing of the evil that had been unleashed on earth, the Maiden-Made-of-Light turned her back upon the world, and the Lion of Night came forth in all his wroth to punish the wickedness of men.

How long the darkness endured no man can say, but all agree that it was only when a great warrior —known variously as Hyrkoon the Hero, Azor Ahai, Yin Tar, Neferion, and Eldric Shadowchaser— arose to give courage to the race of men and lead the virtuous into battle with his blazing sword Lightbringer that the darkness was put to rout, and light and love returned once more to the world.

Yi Ti (TWOIAF)

The Five Forts are very old, older than the Golden Empire itself; some claim they were raised by the Pearl Emperor during the morning of the Great Empire to keep the Lion of Night and his demons from the realms of men

Yi Ti (TWOIAF)

These references to the Long Night and Azor Ahai certainly point to some confrontation with the 'Lion of the Night and his demons', or the Others.

So couldn't the Westerosi just sorta vacation in Essos while the White Walkers have their way for a while and then come back after the planet tilts back closer towards the sun?

The Long Night, if the histories are correct, lasted for a generation and ended only when the Others retreated back to the Lands of Always Winter. I've always assumed they have some arcane abilities, either inherently or through magic, which can affect the weather. Not that it matters because, as I say above, it seems that the Others did make it to Essos. Very, very far east Essos, even.