Is it possible to become the Thane of both Imperial and Stormcloak controlled holds?

I understand that there is the possibility of the Stormcloaks capturing a hold, or city, such as Whiterun. Is it possible to be both the Thane of a Imperial controlled hold and a Stormcloak Hold, if you are allied with neither faction?

Solution 1:

Yes.

The only Hold which you cannot become thane of without choosing sides in the Civil War is Windhelm. You must resolve the Civil War, one way or the other, to be named Thane in Eastmarch.

Other than that, you can become Thane of any hold by doing other quests, unrelated to the Civil War, or by advancing the Civil War to a point where control of the hold in question changes hands, at which point, you will be offered Thaneship automatically.

Solution 2:

Yes, you can become Thane of a Stormcloak hold and a Imperial hold, Ex: You can be Thane of Falkreath (Imperial hold) and Thane of Dawnstar (Stormcloak hold) just by doing favors for the people and buying a house or piece of land if you have Hearthfire DLC.