This question gets asked a lot, because the book has an ambiguous ending. Please see the link below for some answers.
Personally, I think they both die.
That's your choice.
There are many ways what happened to Jonas and Gabe. The last thing that happens it that they ge on the sled and go down the hill. It says in the book that Jonas can feel warmth near his feet. As he goes down the hill, he can hear music. He knows his close to 'Elsewhere'. So teh story can end that he went ot another Scoiety that doesn't have the Utopian society in it.
Or, logically, they can't really stay in teh snow for that long and also when Jonas is transmitting Memory of Snow to him and they do become cold. They run out of food, and personally, i would die in that condition. The story can also end for them both dying for hunger, weakness and coldness.