Winter is a season that can last for years, possibly even decades.
This is true for summers as well, but the seasons are not binary, Spring and Fall exist as well.
This is backed up by many other characters point of views.
Old Nan tells us in "Lord Snow" (S01E03);
"Oh, my sweet summer child. What do you know about fear? Fear is for the winter, when the snows fall a hundred feet deep. Fear is for the long night, when the sun hides for years and children are born and live and die all in darkness.
Tyrion reflects on the seasons in his life;
"As you say, my lord." He had been born in the dead of winter, a terrible cruel one that the maesters said had lasted near three years, but Tyrion's earliest memories were of spring.
"When I was a boy, it was said that a long summer always meant a long winter to come. This summer has lasted nine years, Tyrion, and a tenth will soon be upon us. Think on that."
A Game of Thrones - Tyrion III
Grand Maester Pycelle rambles some history;
There were fools, even in the Citadel, who took that to mean that the Great Summer had come at last, the summer that never ends, but in the seventh year it broke suddenly, and we had a short autumn and a terrible long winter.
A Game of Thrones - Eddard V
There is even a time called the Year of the False Spring which expanded in the books but made its way into the show in the Histories & Lore: House Reed
When he was a young man in the Year of the False Spring, a great southern lord held the largest tourney Westeros had ever seen in the largest castle Westeros had ever seen.