To climb a grade in snow, momentum and controlled wheel spin are my allies.
At the onset of slip, I either cut back just slightly on the throttle, or “blip” it to dig down to coarser surface. The choice depends on conditions, and is a heck of a lot easier to learn/feel than describe.
My Avalon Traction Control fights you every inch of the way. As soon as it detects impending slip/spin, it apples the brakes and completely closes the throttle. Feels like someone reached over and turned off the ignition. All momentum is lost, and the game is over (back down and try again). Disabling the TC is like night and day . . . what was previously impossible becomes easy. Original Michelin all season tires here as well.
Perhaps the software was improved after ’05, which could explain why Tom in Tacoma is able to manage OK in serious snow country. There was a long thread of similar complaints over on the Edmunds forums back in ’05.