I think I may have found a more likely inspiration for Balto 3's plot.
Not too long ago I stumbled upon a movie that really got my attention. It was an American-French drama film called Wings of Courage and one of the things it had on the cover was a bush plain in a snowy mountainous environment.
Here is the cover:

The name and cover alone made it seem very similar to the third Balto movie so I decided to read what it was about. It turns out that the story is based on a true story of a group of French bush plane pilots in South America that start a company to provide air mail service between South America and France in 1930. One of the pilots, Henri Guillaumet crashes in the Andes mountains during a fierce snow storm and has to walk out on his own. Meanwhile, his wife and dog at home are anxiously waiting for him to return home.
Whether Balto 3 gained inspiration from the movie or the real story is anyone's guess but the similarities just seem a little too close for it to be a coincidence. I haven't seen Wings of Courage, but after reading about it, I'm very tempted to watch it.
If you want to read more about Wings of Courage, here's the link for it on Rotten Tomatoes:
http://www.rottentomatoes.com/m/wings_of_courage/