Saddles are a rare item in the game, being found only in chests inside dungeons, abandoned mineshafts, Nether Fortresses, Desert and Jungle Temples, in blacksmith chests found in NPC villages, or by trading with a villager. Also, saddles can be "caught" with a fishing rod. Prior to horses being added, Dinnerbone stated he will not be including a crafting recipe for saddles.
Horse armor [...] can be found in dungeons as well as Nether fortress chests, Village Blacksmith chests, Jungle Temple and Desert Temple chests, and in abandoned mineshaft minecart chests. Horse armor protects the horse from attacks. Horse armor cannot be crafted.
You can't breed pigs with saddles but you can easily attract pigs by holding carrots (PC) or wheat (Xbox) in your hand. Breeding unsaddled pigs is as easy as feeding them that food.
You can attach a rope leash to it and guide it home that way. A leash is made with string and slime, as follows:
If you need to take a break, you can tether the horse to a fence. This allows you to wander off and do whatever you need to do. Provided you remember where he/she is, you can return and get the horse back later.
Best Answer
You cannot craft saddles or Horse Armour, but saddles can be found in other places than dungeons, for example through trading or fishing.
From the wiki page for Saddles:
And Horse Armour: