The entrance is in the guise of the Queen's castle as usual. You wend your way through the castle as the queue and you then reach the load area. The Dwarf-named mine cars seat six instead of four. Behind the load area is a big mural, showing Snow White and her friends, both Dwarfs and forest animals alike.
The mural for the ride in both parks will be different between them. Here's the one at Disneyland:
http://img248.imageshack.us/my.php?image=muralyn7.jpg.
And here's the one at Tokyo Disneyland:
http://disney.wretch.cc/Gallery/c01/p20.jpg.
As you board the ride vehicle, you hear the Dwarfs providing the safety spiel. Then once aboard your car, it moves through the first scene: the Queen's castle's courtyard, where you pass by the wishing well and Snow White dressed as a scullery maid. She is sitting on a flight of steps where she is singing "I'm Wishing" to a small flock of doves. The Prince on horseback watches from the other side of the track.
Then you turn away from the castle into a dark forest. Here, you see the huntsman and Snow White as he warns her to flee. Then you pass by the usual scene of the scary forest, which is pretty much the same as usual, only MUCH shorter and involving the addition of a log that falls down toward your vehicle, almost hitting you on the head. Plus, the flying bats are much more convincing now. There are also evil eyes everywhere, too.
Leaving the forest, you then go through the Seven Dwarfs' diamond mine, where you see the Seven Dwarfs working, singing "Heigh-Ho". Here's an image to give you an idea what the Dwarfs inside will look like:
http://www.disneylandpostcards.com/fldwarfs.jpg. One of the Dwarfs also tries to stop a runaway cart full of diamonds from crashing into your cart. It kind of looks like a cross between both versions from Disneyland, and by both versions, I mean both "pre-83 and post-83". So it's kind of the best of both worlds.
Then you head out of the mine and pass by the Dwarfs heading for the cottage, singing "Heigh-Ho" still. You then enter the cottage, where you see the Dwarfs and Snow White dancing together to the music of "The Silly Song". Here's a picture to give an idea of what the scene will look like:
http://www.tokyodisneyresort.co.jp/tdl/images/pg/fantasy/fantasy_atr02_ph1.jpg.
Upon leaving, you pass below a tree with two vultures perched on it and enter the ominous castle of the Queen. Here, you encounter the Queen with her back to you as she turns into the Witch with the same effect as in Florida. You hear her saying, "Magic mirror on the wall..." and then she turns around and you see that she's become the Witch while she finishes her line with, "I am the fairest one of all!"
After this, the dungeon scene that follows is the same as the other rides, but as with the forest scene, it's much shorter; it only shows the jail cell with the skeleton and the Witch at the cauldron brewing the poison apple while the raven looks on.
From there, you head back to the cottage where we see the Witch handing the apple to Snow White. "Have a bite, deary," she says to Snow White inside the window. You then hear Snow White gasping for air and as you pass by a side window, you see a silhouette of Snow White as she faints while the Witch yells with a cackle, "Now
I'm fairest in the land!"
Then we hear the Dwarfs saying that they're going to stop the Witch. "Quick!" one yells. "She's up on the cliff! Let's go!" You then go to the usual scene of the mountain cliff where you see the Dwarfs on the incline as they stand before the Witch, who yells, "You meddling fools! I'll crush your bones!" You see the usual scene of the Witch attempting to roll a boulder down the hill to crush them, only to meet her own end when a bolt of lightning knocks her off the cliff.
You then go through Florida and France's closing scene, where Snow White and the Prince are on the bridge and the Dwarfs are on the steps of the bridge with the castle in the sunset on the one side of the track, before arriving at the unload area.