Birmingham had a bit of snow yesterday, which snarled the whole area up.
It took me 3 hours to do a 10 mile journey.
I was listening to Radio WM, people were phoning in with traffic reports, and then a plonker came on and said :-
The reason cars are getting stuck on hills is because they have their TC control ON, they need to turn it OFF
.
So the presenter took this up, and advised everyone who had TC control to turn it OFF.
I had no trouble on any hill, TC on, Snow button on. 
The V6 was far more stable than my old 2.2 that hadn't got TC.
See you at the bottom of my street and see if you get up the hill in your Omega TC on or off. There's only so much grip on compacted snow/ice 
My house is up on a hill on a rocky track with sharp-turns, dips and some quite steep-rises:
Without snow chains and TC on; the car rapidly loses momentum on the icy rises and will get stuck (esp. on the bends when the diff-torque favours a side).......
.....Without chains and with TC off; I can keep the momentum up and press on.
....with chains fitted it really doesn`t matter either way. 
Debs studded tires will do the job (++ this signs done by a cat
) and miggy will be more comfy on the steering and vibrations..
As good as studded tyres are cem, they are a waste of money in this country.
We had an SRI cavalier fitted with them at work on spare steel rims and it was found they were fantastic when the snow first fell if the wheels were fitted at work, once the tarmac was showing again the wheels need to be changed ASAP or the studs gring down in next to no time.
The ideal situation would be to have a pair of these in the car at all times, and all neccesry tools like and exhaust drin airbag/jack, quick lift and electric wrench to enable a quick pit/tyre swap.
Sadly that just wont work by the road side, plus weather predictions are poor and you may end up friving round for days on studded tyres based on a weather forecast that was wrong.
My local area (Netweather for example) forecast 96, 95, 92, 92, 86 and 83% of chance of snow starting friday, friday there was a light dusting that came and but london had 3" and Debs got 2'.
So for me it would be my GLS on M+S tyres for winter and the Elite for the rest of the time, but swapping tyres to suit the weather is not allways possible.