Are there restrictions for how many items a mount can carry? There is only 1 slot on the character builder for mounts. I don't understand why I can't have an enchanted saddle, and shoes. They're on totally different areas.
Yes; there is, according to the rules, only one item slot for a mount. This is why the Character Builder only allows you to have only one item on the mount.
I would agree that this is a strange limit, since there are bridle, saddle and horse shoe magic items. Each is a different part of the animal.
There isn't any reason you can't house-rule this and write items down on the character sheet. You will just have to do the math manually for these extra items.
Mounts have one slot for a usable magic item.
Adventurer's Vault, where mount-slot magical items were first introduced, lays it out pretty clearly:
A creature serving as your companion or mount has a single magic item slot that you can activate using your own actions (and not the creature's).
-- "Companion and Mount Slot Items", p.122, emphasis mine
Emphasis on usable.
The limitations around item slots noted in the Rules Compendium may or may not help you here:
Item slots represent a practical limit to the number of magic items a character can wear and use. [For example, a] character can benefit from only one magic item worn in the arms slot even if the character can physically wear bracers and carry a shield at the same time. [...] The character benefits from the item that was put on first; any other item put in the same item slot doesn't function until the character takes off the first one.
-- "Item Slots", p.276, emphasis mine
This might make it conceptually difficult to swap out a set of, say, skystrider horseshoes if you wanted to use another item your mount was wearing, but keep in mind the form of magic items isn't absolute, especially if you have the Transfer Magic Item ritual, so you can probably work with a version that's less securely attached.