I have never driven my LS in snow so I don't know how it works with the traction control, but I have driven many different cars in snow over the past 30+ years and the first rule is...
You do NOT need more power to get around in snow. Gentle and easy touch is what gets you around.
The traction control is doing it's job when you say no matter how hard you push the gas, you get no power. The computer is cutting power to prevent wheel spin which is what you would get with lots of gas or no traction control. You could just push the button to turn it off, but then it would be up to you to be easy on the gas.
Also how are your tires? Tires with little tread depth are no good in snow. You need deep treads or better, blocky open treads to throw out the snow that tries to build up in the grooves.
I drove a 96 Impala SS with big fat tires(which are supposed to be bad in snow) for many years thru snow and ice. 90% of the time I was able to do my commute, even sometimes thru some local "mountains" where the snow and ice were worse, but fewer cars stuck on the road. The key was VERY light gas pressure, slow control movements, No twisting the steering wheel or jabbing the brakes.
I have read many other postings about the LS in snow and most of those guys swear the LS is great in snow and the traction control is a big part of it. I think you are just overpowering the car and the traction control is pulling you back.
So, Slow and Easy will probably get you there quicker than pedal to the metal. And always remember, Stopping is way more important than starting.
Just my experience,
Jim Henderson