Any sold at a physical ski shop. You will make a face at the price. You will reconsider the sketchy ones for their price. But the ski shop ones will last significantly longer.

Ryan Tilley (an AMGA-certified mountain guide) has a long and detailed guide of different sorts of boots and what to look for in each type[1].

[1] https://www.youtube.com/watch?v=RFKC0BynjxY

The key word you’re looking for is a "pac boot" depending on where you live you can get insulated, but honestly unless your live somewhere super cold and snowy, you probably don't need insulation. if you put on warm socks, keep snow out of them, are moving around, and aren't outside for hours on end you'll probably be fine even in really cold weather.

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.

There are many brands making proper shoes/boots for winter hiking. I would recommend taking a look at Haix, Lowa, Salomon Quest series, Lundhags and Meindl.

I prefer military boots, they have no branding and are typically designed and tested for decent longevity and comfort. My current ones are Bundeswehr surplus, I believe Meindl produced them. They cost about 60 euros or so, never been used.

Pick a size larger than you would usually do, unless they're explicitly designed as winter boots. In cold weather you'll want wool socks as well as regular socks and that requires some extra space.