1999 Mazda Protege driving in snow

I recently bought a used car. The tires are all season radials in decent shape (not worn). The car (a 1999 Mazda Protege ES) has a lot of trouble moving in the snow. This is particularly bad when trying to back up. I thought it perhos the was the type of snow we recentky had that made this bad (very wet and heavy snow) but other cars (many not all wheel drive or SUVs) handled the snow fine. It does not appear to be a steering issue because I was simpy trying to move backward and forward. The car just would not budge even in the middle of a sttreet thhat was not all that deep with snow. When in normal conditions it runs fine My friend's car runs fine in snow and when I checked my tread against his they were about the same. What might be the problem? Thanks much