Does anyone know what the name of this older movie is? It is about a boy and sled racing dogs, and they die at the end but not before almost winning the race.

Are you thinking of "Stone Fox" which I watched yesterday?
The Dog dies just before the finish line, and the Boy carries him across the line to win the race. Stone Fox is an Indian with a team of Samoyeds , and he has never lost a race, but he stops the other racers and allows the boy to carry his dog over the line, to win $150 so the boy can save his Grandpa's farm. Buddy Ebsen is the Grandpa who is recovering from a stroke. Hope this helps you out