Unlike previous Elder Scrolls games, there seems to be no direct penalty of spell failure chance or mana cost for spell casting when using armor. Instead, players are incentivized to use mage robes by placing an enormous magicka regeneration bonus (50% to 150%, depending on item level) on college robes which cannot be duplicated by enchantment.
For a caster, the choice between armor types is about mobility and the cost of "sunk" perks you won't use. Heavy armor slows the wearer's movement and weighs a great deal (until you get Conditioning ) but provides better protection and dramatically reduced stagger (Tower of Strength ) and a 10% chance to reflect melee damage (Reflect Blows ). However, while Conditioning is an absolutely required perk for a caster, the perks leading up to it are of debatable usefulness at best.
Light armor has a much smaller movement penalty, and the Unhindered  perk which makes it weightless is available much earlier and with more useful prerequisites than its Heavy Armor equivalent. In addition, the Wind Walker  perk may be extremely useful to a hybrid mage-warrior, as you will not have as many level-up points to invest into stamina or enchant slots to spend on stamina regen as a pure fighter would. Deft Movement  (10% chance to avoid all damage from a melee attack), the final perk, is of course useful to anyone.
Considering all of this, I'd strongly recommend taking Light Armor for a hybrid caster, but it's not a clear-cut choice and other players may find the advantages of plate outweigh the costs.