Originally Posted by tsl

There could be several things.

First studs don't do a thing for you if they don't have something solid and unyielding--pavement, ice--to bite into. Studs do squat when you're floating over soft and loose stuff.

Second, when you do float over soft and loose stuff, sometimes as it packs under your tires, that packed snow will itselfl slip on the surface beneath. But since your tires are gripping the snow that's now sliding, there's not much you can do.

These are two of the reasons I prefer narrower tires for commuting. I want to sink through to the road so the studs can get a good bite. Off-road, you generally want the opposite--to float.

More generally, cycling in snow quickly reveals how well you hold your line, and whether you've learned to keep your balance by shifting your weight or by steering. (The former hold their line straighter, the latter weave a lot.) If you keep your balance by steering, you'll be considerably less stable in the snow.

Weight distribution matters. Shift your weight back on the bike. When folks say they use MTB skills, this is the first one they use. My first winter I used a hybrid where most of my weight was on the back. It was a rock. In my second winter, I nearly gave up on my Portland because the roadie position put so much more weight on the front. It wanted to plow rather than steer. Once I learned to shift my weight to the back, it stabilized.

Also, if you carry your weight on your butt instead of your toes, you'll be less stable. In other words, support yourself on your legs (and fingertips), not plopped on the saddle like a reclining chair. Another way this is commonly stated is to ride light in the saddle.

Spin, don't mash. It helps you recover your balance faster during the inevitable sideslips.

Try these things in addition to those suggested above and I'm sure things will get better.