So some people say it's heav armor, some say it's light armor. It would be pretty stupid from Bethesda to put the plate perk in light armor branch for a heavy armor, so I'm guessing it's light armor ?
The perk "Advanced Armors" allows you craft both Scaled and Steel Plate. Scale is Light and Plate is heavy. You're right it doesn't make much sense for a Heavy Armor type to be on the Light side of the Smithing tree, but at least it's fairly easy to reach at only 3 points.
Plus how do you make them ? I think the steel plate armor looks THE BEST of all armors in the game. I hate spiky armors, they look childish to me.
(1) Level Smithing skill to 50; (2) gather the http://www.uesp.net/wiki/Skyrim:Forge#Advanced_Armors; (3) ???; (4) Profit.
And... what do you think of light armor vs heavy armor ? To me there doesn't seem to be that much of a difference between the two when comparing stats.
Light Armor enjoys lots of intrinsic advantages over Heavy Armor because of the way equipped armor weight impacts several important game mechanics. The weight of your armor affects: (1) your ability to Sneak; (2) how quickly your Stamina drains while running; (3) your carrying capacity (duh); and (4) your ability to enchant multiple sets of armor for different purposes. A full set of Elven armor, for instance, weighs only 7 lbs, which means you don't need things like a Muffle enchant on your boots, or the Steed Stone so you can run farther and carry more, etc. If you're wearing Heavy Armor, you have to "solve" all of those issues with enchants, perks, standing stones, etc. whereas a Light Armor wearer can simply ignore them and focus on other things.
That being said, virtually every type of Armor in the game can reach the armor cap (567 displayed), so wear whatever you think looks best. If that's Steel Plate for you, you'll likely need (1) either the Steed Stone or the Conditioning perk in Heavy Armor; and (2) a Muffle enchant on your boots and the Muffled Movement perk in Sneak (if you want the option of being stealthy). That should solve most of the weight problems.
Edit: Loth beat me to the punch!? Unpossible.