Yes. There are THREE saddles in the Tutorial map, from two dungeons. It's hard to explain the exact spot to go, but it's on the spawn point of the map, in the underground cave systems you can find under the furnace.
I may not have a picture of the area (I refuse to use Facebook, so I can't take screenshots...), but I can tell you where to dig ~straight down~ to hit the Skeleton spawner.
First, go into the "Village" (the one with the castle, not the one with the abandoned Wheat field), and go to the front entrance of the castle (you can take the Mine Cart if you wish). Stop at the STAIRS.
Next, turn around so that you are facing the Red Stone Torch. Take a LEFT along the path of the island and follow the edge of the island, keeping the Castle BEHIND and to the LEFT of you. You should reach a sand section.
Once you get to the END of the little sand section, look for the three little trees right next to the water. You should be on uneven Grassy Dirt at this point. With the SAND to the LEFT of you, the trees to your RIGHT, and the Castle in the UPPER-LEFT of your view, look for the section of ground in front of you, that goes in from the water "three blocks".You should BARELY be able to have both the castle and the branches of the tree in your line of sight if you are on the same plane as the water. Make sure you are in the same row as those three blocks of Gress/Dirt!
Go up TWO steps on the grassy dirt, and move away from the water, until you are "sandwitched" nicely into the little corner. You should now be able to more clearly see the Castle on your LEFT, and two of the three tree trunks on your RIGHT. Now, look DOWN, and start to dig STRAIGHT DOWN! You should hit Stone/Cobble stone after about three blocks of Dirt. If not, don't worry, just keep digging STRAIGHT DOWN.
After "twelve to fifteen" blocks of alternated Dirt and Cobblestone, you should fall down into a cave system (you'll start to hear monsters, on "Easy+") STAY WHERE YOU ARE, DO NOT MOVE! Thankfully, the fall will NOT kill you, only harm you a little bit.
Now, CONTINUE DIGGING STRAIGHT DOWN. After busting through a few more blocks, you should land directly in the Skeleton Dungeon. Loot the Chest, and hope for the Saddle.
I HIGHLY suggest doing this on "Peaceful", because without any light sources, the Skeletons WILL slaughter you in a flash.
I've just tested this on an alternate Gamertag, and found it instantly using this "guide". So I hope you can, too.
Sugarcane was also another item that had issues during World Generation and was missed from the Tutorial Level.
This will be added to the Tutorial level along with Clay pockets when 1.7.3 is released.
Yeah... I should have pointed out that Treasure Chests ~are~ random... I ended up with three Saddles, and three Cocoa Beans... and like four Buckets, when I looted my Dungeons... but thankfully, seeds do seem to always spawn locations identically. Because of this, I was able to help friends find clay, and point them to where the Dungeons are hidden.
Oh... and I'm sure the answer is obvious... but will I have to recreate the Tutorial World after 1.7.3 for the Sugar Cane to spawn? It's the only thing my little world is missing, and I've already built massive amounts of irreplaceable structures and cave systems.