I think the CCs are very good in snow. I have CCs on the RX 350 and put Blizzaks on the Kia - the RX 350 made it up the snowy driveway with AWD with absolutely no problem. The Kia with FWD had to have a running start and if you stopped in the middle of the driveway, you weren't getting up the driveway. So AWD with CCs is significantly better than FWD with Blizzaks IME.
Most AWD systems cut power from one axle and distribute to the other axle.
Back when I lived in NJ, at the top of a steep hill and a steep driveway, the only cars that made it up where Subarus with all-season tires (back before all-weathers became popular). My FWD wagon with Nokian Hakkapeliitta RSI's couldn't make it up, unless I had chains on.
So, it doesn't say much that all-weather on AWD vehicles are better than FWD with nordic winter tires for climbing a hill.
On my AWD Highlander, while there is no physical connection between the front axle and rear axle, as my hybrid as an electric rear motor powering the rear axle...
The CC2's had trouble making a u-turn in this mess (driving to Big Bear Lake, CA). It was fine one the plowed snow surfaces, but the deep snow, 3-wheel spin, until it caught a little momentum on the packed snow I made.
My old Nokian WR G4 were a lot better on the deeper snow conditions. But that tire started life as a Central European winter tire, and Nokian did whatever to call it a "All-weather" tire for the US/Canada market.
And that wasn't the first time I noticed that CC2's suck in deep snow.... after the first round of blizzard came by in December 2021, with fresh CC2's, getting my car out after the plows came through, the CC2's had a little trouble until I got the front axle onto plowed snow, so I can park my car in a plowed parking spot, so the plow can finish its job.
The 2nd time was later in the winter season in the Cottonwood Canyons, in Utah, where I was brave enough to blaze a trail in deep snow and lost traction, so I was effectively stuck. Switch to "Trail mode" and got myself unstuck, due to the traction control programming of trail mode and got myself back to plowed snow territory and was fine since.
So the CC2's have a weakness, as I pointed out, even with 2 axles driving the wheels.