In Pathfinder, can Animated Dead (Skeletons in this case) be equipped with different weapons and armor?
This includes un-equipping, and then equipping better gear.
Typically the animated dead created by the animate dead spell (usually skeletons and zombies) will wear whatever armor their controller orders them to don, carry whatever shields they're ordered by their controller to carry, and wield whatever weapons they're ordered by their controller to wield. However, merely ordering them doesn't grant the creatures proficiency with that armor, that shield, or those weapons, but such creatures may already possess such proficiencies.
For example, the typical typical skeleton or zombie doesn't have any armor proficiencies or shield proficiencies, so it will suffer any armor and shield's combined armor check penalty on, for example, attack rolls and initiative checks (which are Dexterity ability checks) in addition to the armor check penalty on skill checks.
However, the typical skeleton or zombie retains the weapon proficiencies it had in life, so, for example, it usually behooves the necromancer looking for a warrior-type skeleton to dig up the bones of Sir Deadalot, a fighter, and animate those instead of digging up and animating the bones of the wizard Archmage Hessodead.
Specific creatures that are created through the use of the spell animate dead must be examined individually to see if their stat blocks include any specific armor, shield or weapon proficiencies. If none are listed, then that undead follows the general rules of the type undead, making it proficient only "with whatever type of armor (light, medium, or heavy) it is described as wearing, as well as all lighter types[,] shields if [it's] proficient with any form of armor…," and "its natural weapons, all simple weapons, and any weapons mentioned in its entry."
(This means, for example, that the Medium skeleton is proficient with simple weapons due to its type, the light armor and the scimitar due to them being mentioned in its entry, and shields due to its armor proficiency.)