Baffin make some of the best cold weather boots. We use them in Antarctica, though you probably don't want the chonky -70C rated ones. I have some lighter boots rated for about -40 and they're great. Really any good gore tex mid-ankle hiking boot is probably fine. Whether you need cold rated boots is going to depend on where you're walking.

Your main concern is to stay dry and minimize snow incursion. Either wear ski pants that act as gaiters, use gaiters or use boots and socks that are high enough that you won't get snow down the sides.

If you buy boots with insulation, try not to compress it. Otherwise be aware that if you don't keep moving, your boots will eventually cool to ambient and it's pretty hard to get that temperature back up.

Check grip? Hard to test but warm doesn't necessarily mean any good on slick ice. Spikes work well if you're going on a hike and there's a lot of packed snow mixed with ice.

Don't forget good socks. Doesn't need to be anything fancy, but wool is by far the best material (not necessarily merino as it tends to be too thin). You may need to size up because of the extra padding.

Also luxury, but fan assisted boot drying/warming stations are great. They make quite a big difference if you go out a lot because moisture build-up takes ages to dry otherwise.