tires for snow riding

So I went out to jburg today. Sloppy mess. But not the mess I was expecting. I thought it would have been muddy. It wasnt. It was wet snow, 2-4 inches deep. I had to bail after about 30 minutes. Not much fun at all. My shoes are not waterproof. I could only imagine what the FNHR ride would have been like. Not very happy.

Anyways, I currently have a 2.3 up front and 2.1 in back, both nevegals and low pressure (25 psi or so). Well, I had practically no traction. Any upgrade and I had to walk. Flat sections were hit and miss (mostly miss), but downgrades were ok. Squirrely but ridable. Fun actually. But not nearly worth all the effort.

So my first question is "Is this what riding in the snow is all about?" If so, I think I will stick to ptex on the snow thank you very much lol. If not, then what kind of tires do you guys run? Width? PSI? Studded? If so, how big are the studs? The studded tires I seen wouldnt nearly have enuff depth to the spikes in the snow I attempted to ride in today.