Actually more rubber on ice is better, unfortunately more rubber on snow equals less per square inch of pressure to compact the snow, which makes you not go.
I have pulled my 29 foot wellscargo with both my 04 drw dodge and my 03 srw dodge, the srw with michelin xde m/s 245/70 19.5's and the drw with michelin ltx m/s 235/70 17 the DRW was much better for getting out of the parking lot.
I now have a '10 dodge srw and still run 19.5's in the summer but full studded snows general 285/70 17's altimax arctic's in the winter, now it will go places in 2 wd that it wouldn't go in 4 wd before.
Toss a set of snows on a drw and leave a all season srw equipped truck in your snow dust.