On I-80, heading into Donner pass as you go through lake tahoe, CHP/Caltrans does indeed check every single car as it drives through ... during dangerous driving conditions, that is.
They usually funnel the interstate down to two lanes and have two guys waving cars through, one by one. They make sure that you either have a AWD/4WD vehicle or that you have chains on. Theoretically they are checking that AWD/4WD vehicles, without chains, also have snow tires, but that isn't really happening - they can't tell that at the 8-10 mph speed you roll through at.
It may also interest you to know that there is a lively cottage industry of chain rentals and installers just prior to these checkpoints. You can pull over just before the checkpoint and for $40 someone will quickly (and properly) install chains on your car, and then for another $20 at the other end of the pass, someone will quickly take them right back off.
This is regular and organized enough that you could absolutely drive through Donner pass in a blizzard, with no preparation whatsoever (other than $60 in cash).
It may also interest you to know (it interests me) that other, higher passes, with just as much potential for snow/blizard don't have any of these checks or precautions. You can drive yourself right over vail pass (I70, Colorado) with whatever drivetrain or tires you like.
Also, if you don't have them and you get into an accident, it's expensive fine time :P