The laws are the same in all of Tamriel, High Treason is death. Though the Nords don't want trials, they don't like trials, sitting around in a court talking for ages isn't their thing. Violence is a part of Nordic culture, it's accepted and common place. Their politics also reflect this, on how you send a man your axe instead of talking.
Tamriel law has it's founding since the First Era I believe, Imperial law is what keeps the provinces in check. Otherwise they would rather kill each other than work together. Skyrim prefers to invade High Rock and Hammerfell than work with them or aid them. Once the Jarls of Skyrim kill themselves it brings back the bad old days, the Nords agreed with the Pact of Chieftains, the war of succession left a pretty bad stain on Skyrim's history when the Jarls went into Civil war on who was to become the next High King. They never recovered. Bringing back a tradition which allows you to challenge a Jarl for their title is what brought on Clan wars. With that in place when the Stormcloaks take over, you'll see many Holds change hands, since it is okay for Ulfric it will be okay for any Nord to exercise their right to challenge. The Bandits are going to love that, why be an outlaw when you can kill a weak Jarl and become Jarl.
"That's what started this whole war. The Empire couldn't ignore that. Once the jarls start killing each other, we're back to the bad old days."