I've played a lot of different characters, played both sides of the civil war, and many of my characters just stay out of it altogether, but my main PC joined the Stormcloaks. A decision I later regretted. Not because I felt he joined the wrong the side, but I just hated the irreversible changes that the CW missions had on the environment. However, so far as feeling that the game is steering you to one side or the other, I honestly feel that it's trying to steer you more toward the Stormcloaks than the Empire.
From the very start of the game, you're shown an ugly side of the Empire. You're captured for no reason, and even though you're not wearing any uniform, not on any list, and no one has any idea who you are or what crime you've committed, they elect to liberate your head from your shoulders because reasons. You see the Thalmor there, and get a sense of the Empire and Thalmor having a relationship, and who comes to your rescue? A Stormcloak. After leaving Helgen, not too far south west, you find a shrine of Talos where some worshipers carrying no weapons have been slaughtered. Obviously by the Thalmor. You stumble across justiciars escorting political prisoners, hear tales of kidnappings, and all this is under sanction from the Empire who is turning a blind eye to it. Even durring the peace council at HH, Tullius shows up with a Thalmor agent, which he had to know would be a slap in Ulfiric's face considering his past, and the brutality he endured by them.
Over all, I felt the game wanted you to relate more to the rebels. The idea of being religiously persecuted, hunted down, tortured, and see this as your motivation to join the civil war. While I personally agree with the idea of the rebellion, I have to admit the game is stacked against the Empire.