Honestly it's all RP. You could probably make the argument for either one. The problem is that the Civil War questline doesn't grant you the ability to work as a random mercenary. The dialogue actually makes you a commanding officer etc.
Also - if you wanted to continue mercenary work for a long time - you would run into an issue where a lot of the forts you conquer no longer become available as radiant quests because you conquer them for one or the other faction. A lot of these forts are filled with bandits / necromancers prior to the Civil War starting.
If you want to roleplay a mercenary. I'd start by visiting the different Jarldom's of Skyrim and offering to do work for them. You can speak to the stewards and innkeepers. They will continuously refresh with offers to slay people etc.
This would play more into the mercenary role as the Jarls hire mercenaries to do the dirty work around their feifdom's while their soldiers are off fighting the Civil War.
If you go through with the MQ and do Season Unending, what happens to those forts?
IIRC, you can basically act like a merc to Ulfric if you side with the 'Cloaks, and he even has dialog lines to that effect when you insist on pay for services rendered. With the Imperials, you're basically enlisting in the Legion as a commando (a la the Blue Stripes in Witcher 2). One of the reasons the Legion wants to keep the Reach out of the Stormcloaks' hands is because they expect that silver to go into hiring mercs should that hold end up going Stormcloak.
Just don't see a Nord siding with Ulfric as a 'Cloak as a mercenary, would probably just be interested in the war effort. Are you roleplaying a total scoundrel?
Nord != automatic Stormcloak supporter. It's called a Civil war. Not a war against foreign occupiers. Heck, the most focal hold of the entire campaign was initially ruled by a jarl (IE: a nord) who didn't care at all for the civil war.
I see your argument. I just lack the imagination to roleplay that much of a scum! Taking advantage of the plight of his own people to profit!
Galmar says they don't want hired thugs, only committed fighters. But I guess either side would make exceptions.
http://cs.uesp.net/index.php?game=sr&formid=0x000e1b22
Yeah but Galmar is unrealistic and an idiot. Ulfric at least knows what it takes to win a war. If Galmar was leading [censored] would be over in a week.