Nope. Most of the heavy armors look so bulky and ridiculous.
Maybe go for steel with the nordic boots and gauntlets, or the carved nord armor (provided you have the DLC for it), or the ancient Nord armor. Or you could use both armor types. It wouldn't be very efficient leveling in regular game play, but it can be done. An easy way to level an armor skill is to let a giant bash you for half an hour. Just temper the armor as best you can, bring healing potions/spells, be well-rested, and use the relevant standing stone.
I wouldn't mind if the Stormcloaks had their own heavy armor, but I don't feel I miss out on anything playing the Stormcloak side as a heavily armored character. The Stormcloaks is more of a militia/make-shift army, mostly using the same armor the city guards of Windhelm already did. I don't feel out of place using my own armor when fighting at their side. Especially since I usually wear a nordic type armor when fighting at their side, like Steel with pauldrons, Cuffed Boots and Nordic Gauntlets. In truth, I would have preferred the Stormcloak commanders to not have a standardized armor, and that the Bear armor was something Galmar Stone-Fist wore.