The change of seasons in Westeros

On the matter of the strange change of seasons in Westeros – summer for a variable number of years, then winter etc. – I have a theory. (Although most likely, I’m not the first one who has this idea.)

The Hound saw "a mountain that looks like an arrowhead" in the flames, and later north of the wall, they arrvied at that mountain. We saw the same mountain in the flashback that showed how the first White Walker was created, compare the images here:
https://www.inverse.com/article/35759-game-of-thrones-season-7-beyond-the-wall-mountain-arrowhead

But in the flashback, the Children of the Forest aren’t in an icy landscape, they are surrounded by green grass. So, my theory is: There simply is no natural winter in Westeros. Both the icy north and the change of seasons are purely magical and somehow connected to the existence of the White Walkers. If the Children of the Forest hadn’t created the Walkers, all of Westeros would know only summer.
How this works exactly is still uncertain. The north is the WW’s home, so it’s always frozen. But for example, there were there lots of winters south of the Wall when the WW didn’t show so obviously winter does not only come when the Walker jump into "active mode", so I currently have no idea what determines when winter will come and how long it’s going to be. But hopefully this will be revealed before the show is done. (Well, IF my theory is correct.)

What do you think about that?