Wizards often wear decorative pieces of armour such as pectorals, vambraces, and heavy belts. These are not sufficient to give an armour saving throw and do not affect the wizard's ability to cast spells. Wizards who wear more armour or carry shields, including magic armour and shields, cannot cast any spells. This includes spells bound in magic items. The exception to this is Chaos Armour which does not affect a Chaos Sorcerer's ability to cast spells or use magic items.
Note that armour does not prevent a wizard using other magic items, and it does not prevent him using cards from the magic deck to dispel, destroy magic, etc. Armour worn by a horse does not affect the wizard either, so a wizard riding a horse with barding will have a saving throw of 5+ (6 because of the horse and +1 makes 5 from the barding).