You also have to figure in the force required to push the tire through
the snow, since any reasonable sized tire is going to sink in to some
depth.  It takes more force to push a wider tire through the snow, more
if its dense spring snow.  I've had my truck buried up to the axles in
spring snow and I stalled out a 9000 lb. winch trying to pull it
forward.  It wasn't until I put the transmission in gear and let the
tires turn slowly, that it came out.   Point is it can take a lot of
force to push something through snow.  

I've run various 33" tires from 9.5" to 15.5" wide on my '85 4Runner and
they all seem to work about as well.  The very wide tires at 2 psi would
let me float up on deep snow better, but it was a lot of work to get
them back on top of the snow if/when you broke through.  You had to keep
making runs at the unpacked snow to get enough momentum to get up and
out of the ruts, then it went good until you hit another softer area or
whatever and sank again.  I find the narrower tires (I currently run the
10.5 ATs) might not float as high, but are much easier to get going and
keep going.  All my current snow driving is up in the northern CA Sierra
Nevada and the snow is affectionately called "Sierra Cement".  May fall
as soft powder, but a few days in the warm weather and sun, it gets
pretty heavy.  It also tends to be deep, no way to dig down to a hard
surface.

What I have found to be important for snow traction is letting the tire
treads pack down the snow under the tire as it slowly rolls forward,
then with the snow locked into the treads, you can use that bonded snow
like a cogged railroad.  A skinny tire, as mentioned, has a longer
footprint for a given inflation pressure that a wider tire, so you have
a longer patch of compressed snow to push off of.  A wider tire won't
pack the snow as hard and the contact patch is not as long and it tends
to be easier to overpower the snow and spin the tire.  On one of our
last club snow runs, there were many vehicles with 33x12.50 and
35x12.50s and on one hill several were getting stuck left and right.
Took a lot of work to get one of the trucks ahead to manuever around
enough to pull them out.  Getting bored waiting, I pulled out to the
side and easily drove up past them made a 180 turn and drove back down
the other side and then back up again.  

Unless you are talking about something like an 18.5/44 Cepek Fun Country
tire, you are not going to be floating over bottomless, soft snow in a
normal vehicle.  In the 33" tire diameter I've run, there is perhaps a
2:1 ratio of actual tire widths and in terms of footprint even less
difference and and unless you are in conditions that are just on the
borderline of firmness where a 15" wide Swamper would stay on top and a
narrower tire wouldn't, it won't make all that much difference.