Like, if you're doing the Civil War quests for the Empire, do you wear the Imperial Armor? Or do you pretty much just use the same set of weapons/armor regardless of who you are questing for at that time?

yeah I like too, helps with rping. Though it svcks that they dont have mages robes for them, good thing theres a mod for it

My character wore Stromcloak armor when I did the Stormcloak side of the civil war. My current charcter is doing the Imperial side and wears their armor too. But none of my characters have worn Dark Brotherhood or Thives Guild armor in Oblivion or Skyrim. I don't think it makes any roleplaying sense for my character to publicly advertise they belong to these factions.

I usually do. But my recent playthrough I didn't don the Wolf Armour even though my dude is a Companion. He wears light armour, you see. I don't think there is a conflict as not every Companion wears wolf armour.

When going through the civil war quests I tend to wear my side's armor. If I join a guild then I only wear the armor if it's actually better (either in looks or bonus) than what I have. If not, nope.

I wear DB armor when doing the hit.
Suppose I am going to kill someone in the streets of Markarth. I take some hooded robes and wear them as I enter the city. When I get to a good spot and prepare for the kill, I put on the DB outfit (I imagine that I was wearing it all the time - it just was under the robes) to help with mobility (I suppose that's the reason we are given the DB gimp suit). When I do the hit and run away, I go to the nearest corner and put the robes back on to disguise myself.

That is hard core. I used to change when I would do my shopping and smithing/enchanting but I got tiered of going through my inventory to find what I want so now If I change it will just be my main armor to clothes and keep armor bracers and boots on.