And they didn't cut it out of the game. All the classes are still there. And in fact, they've made the system more flexible. In Oblivion, if you wanted to be both a warrior and a mage, you had to make that decision right at the beginning, if you wanted it to be equally effective. Otherwise, if you chose warrior and got to be a good warrior and then decided "Hey, I wanna be a mage too", well, you could do that - I did - but with the restrictive major and minor skills construct - which was integral to the idea of classes - you wouldn't be getting character levels very much by using mage skills.
With Oblivion you can get to level 10 as a mage, then decide "to hell with this, learning magic is hard" and put on some armor and go smash skulls with a mace. You still have all your mage skills and perks, without giving anything up regarding being a warrior.
Bullhockey.
You can pretend things are still in the game in your head, but I prefer that it actually acknowledges me in this.
In that, there are no classes in Skyrim because there are no classes in Skyrim.
I do not get to pick from a list, I do not get to choose and name myself and there is no class description for my character.
So you can 'its still in there' till the cows come home, but no, it is not.
Skyrim has no classes.
It doesnt have any flying martian robots either, unless you want to 'pretend' they are there.