The Giver gives Jonas snow because it does not exist anywhere in the community.
For his first memory, The Giver wants to share something with Jonas that he has never experienced before. In one memory, Jonas sees hills, snow, and a sled. These are completely new concepts for Jonas. The Giver also uses this same memory to give Jonas pain, and to help him experience color.
The sled is a metaphor for the memories. The Giver tries to explain to Jonas the burden of the memories, and he says it is like a ride on a sled. Since Jonas has no idea what he is talking about, sharing the memory of the sled ride seems like a good place to start.
"It's like going downhill through deep snow on a sled," he said, finally. "At first it's exhilarating: the speed; the sharp, clear air; but then the snow accumulates, builds up on the runners, and you slow, you have to push hard to keep going, and--" (Ch. 10)
Jonas is thrilled by the memory. Everything in it is new to him. His community has eliminated all weather, and they also got rid of the hills. The memory of sledding down a hill during the snow is wondrous to him. It shows him how beautiful and different the world used to be.
It was very startling; but he was not at all frightened, now. He was filled with energy, and he breathed again, feeling the sharp intake of frigid air. Now, too, he could feel cold air swirling around his entire body. (Ch. 11)
As they continue the training, Jonas experiences many things that used to exist. He notices that the sled was red, the first color he is able to see. (Color was eliminated also). The Giver also uses the same memory to give him pain. Jonas experiences a sunburn, and a broken bone from crashing the sled. The memory that gave him so much pleasure also caused him to suffer. The Giver is showing Jonas that the world used to be more nuanced.
Trying to make things perfect has advantages and drawbacks. You can transport goods more easily without hills, and you can grow more food and keep people more comfortable with climate control. Yet for each thing you gain control over, you are losing something wonderful. This is the lesson we learn through the memories. Some things are worth keeping, even if they are imperfect.