In 3.0, your dwarf would be slowed down to 20 feet if he put on medium armor.
In 3.5e, A dwarf barbarian in medium armor would still move at 30 feet, because dwarves are not slowed down by armor or encumbrence. If your dwarf put on heavy armor, however, he would drop to 20 feet, because heavy armor disables a barbarian's fast movement ability.