The plot of the film is almost completely different from the 1964 TV-special, as are the songs. A baby reindeer named Rudolph is born with an abnormally red, shiny nose to Blitzen and his wife, Mitzi. His parents start to worry that Rudolph will be made fun of because of this, and their worries come true when the secret of their son’s nose is accidentally revealed to Rudolph’s three uncles, Comet, Cupid, and Dasher, along with the rest of the residents of the North Pole.
Meanwhile, two of Santa’s elves Doggle and Boone cross the bridge of the wicked Ice Queen, Stormella to deliver mail and accidentally crash into and destroy several ice statues that belong to her. When Stormella finds out, she closes her ice bridge to the public as punishment, and if anybody dares to cross it, she threatens to create a blizzard so strong it will render Santa unable to deliver presents to children around the world.
A year later, Rudolph is sent to school, where he is ridiculed by everybody around him with the exception of Zoey, a female reindeer that he falls in love with. Rudolph eventually runs away from school because of all the teasing and meets Santa, who accepts him despite his nose and treats him with kindness. Shortly after, on Christmas Eve, after Santa has flown away for his annual travel around the world, Rudolph winds up running into Zoey but his mean and arrogant cousin Arrow, who has also set his sights on the doe, disrupts their romantic moment beneath the mistletoe and tells Zoey to come with him instead which she reluctantly does but as she leaves she smiles over at Rudolph making him realize that she likes him.
Years later, Rudolph has reached adolescence and is about to take part in the Reindeer Games. Zoey gives her pendant to Rudolph to bring him good fortune, much to the chagrin of Arrow, who is now in a relationship with Zoey. Arrow cheats at the games so he may be chosen to become a Flyer (one of the reindeer who pulls Santa Claus’s sleigh) so during the big race he trash talks Rudolph, making his nose gleam and blind Arrow. Rudolph wins the race, but is disqualified because his glowing nose is considered cheating. The disqualification of Rudolph infuriates both Blitzen and Zoey, who confronts Arrow for cheating and ends their romantic relationship. Rudolph overhears Blitzen arguing with the referee elf of the Reindeer Games that his son’s nose was “an accident,” attempting to persuade him that there was no way Rudolph could have controlled his nose’s glow and avoided blinding Arrow. But Rudolph misinterprets it to believe that his parents are ashamed of him, and decides to run away. Zoey is devastated upon learning that Rudolph ran away from home, so she runs off in search of him and even deliberately crosses the forbidden bridge of Stormella, who imprisons her in an icy prison cell.
Meanwhile, Rudolph has become acquainted with an Arctic fox named Slyly and a polar bear named Leonard. He also meets the Sprites of the Northern Lights, a group of singing, colorfully garbed sprites who fly around the North Pole. They tell Rudolph that he must rescue the kidnapped Zoey. They instruct him how to properly use his nose, and Rudolph, Leonard, and Slyly journey to Stormella’s castle to free Zoey. Stormella fulfills her vow and unleashes a humongous blizzard upon the North Pole using her magical powers. However, Slyly stays behind while Rudolph and Leonard enter the forbidden castle.
Rudolph and Leonard make it inside her castle, but soon find themselves locked up in ice prisons of their own. After the Ice Queen goes to sleep, Slyly sneaks into her bedroom and retrieves the key to his friends’ prisons. However, Stormella wakes up and sends her pack of wolves after Rudolph and his friends, cornering them on a cliff. When she threatens to freeze Zoey, Rudolph uses his nose to blind Stormella, sending her toppling off of the cliff, hanging on for dear life. Rudolph saves Stormella’s life by allowing her to grab on to his budding antlers and pulls her back up on the cliff, and the grateful Stromella offers to grant him a wish. Much to the Ice Queen’s dismay, Rudolph wishes that Stormella would turn from evil to kindhearted.
Stormella does indeed have a change of heart but the snowstorm that she created is unstoppable. Boone and Doggle, who were sent to search for Rudolph and Zoey, bring the entire group back to Santa’s Village. However, because of the blizzard Santa is unable to carry out his flight this year but when he catches a glimpse of Rudolph’s nose, Santa asks him to lead his team, to which he agrees. Rudolph guides Santa’s sleigh through the storm, and receives a hero’s welcome when he returns and it turns out to be a merry Christmas after all.
You can read more about the movie here on Wikipedia.