When I backpack in the snow, I usually take a foam mattress AND my inflatable mattress to maximize the R value and provide more separation from the ice and snow.
Don't have a dog to worry about. I have had some slow leaks on the trail (last half of the JMT in '20, for instance). Unfortunately, I've never found a foam pad that works for me by itself (I'm a side sleeper).
I only recently became aware that people sometimes bring both inflatable and foam. What is the thinking? That an inflatable is just too risky by itself? Get a hole and you are basically sleeping straight on the snow? Or is there more to it than that?
I've got some thoughts. The problem with camping on the snow is that every night feels like a night spent in a cold basement with a groundwater problem. The more insulation you bring, the more pleasant the experience. If you bring two thinner pads, you can spread out both pads, to create some additional dry real estate, to perform camp chores (meal prep, etc.). Later, when it's time to hit the sack, all available pads are shuffled into place, underneath the bag.
I've spent comfortable nights on the snow using just a single closed-cell foam pad. First I lay down a sturdy plastic ground sheet. On top of that I place a full length (72 inches long) foam pad, such as a Z-rest or a Ridgerest pad, folded in half. I place this doubled-up pad underneath my torso, squaring it between my shoulders and my hips. Underneath my legs I'll shove a grunge bag containing my boots, plus my empty backpack. That's enough to keep my legs off the snowy ground. Doing that also prevents my damp boots from freezing solid overnight. If I'm cowboy camping, I tuck my sleeping bag into a bivy sack for some extra warmth. The neat thing about snow-camping is that you can dig hip wells, and sculpt the bed the way you like it, without feeling like a slob. I'm a side-sleeper, too, so this is a real perk.
Everybody's metabolism is a bit different, and the above setup might leave you cold. Still, I've never felt like I was losing heat into the snow underneath me. It's the frigid air all around, that's produces the chilling effect.
