This right here. I drive a tiny old rear wheel drive 4 cylinder pickup which is arguably the worst vehicle for winter driving. The only thing it has going for it is that it does have a bit more ground clearance than cars. I live in Minnesota and work nights so I often get off work before the plows have cleared the roads. As long as I have a good set of snow tires on that truck, a couple sand bags in the back, and drive carefully, then it can and has trecked through roads covered in nearly a foot of wet snow like a champ. I've had to give rides to multiple people who planted their big 4x4 SUVs in the ditch with that little truck.

Also because OP mentioned it but you didn't say anything in your post, wide tires aren't necissarly better in the snow. The best winter vehicle I've ever owned was a tiny 90s Mazda pickup that actually used unusually narrow tires compared to modern vehicles. Wide tires are great for mudding or off roading because they distribute weight over a larger area and help prevent you from just getting stuck in your own ruts. However when it comes to snow you actually want to sink farther down in the snow because there is road underneath so you don't need to worry about digging ruts. So narrower tires will concentrate the weight of your vehicle better and give you a better chance of digging down to a solid surface rather than skating across the top of the snow. With wide tires they wind up distributing the same weight over a larger area so you just wind up with more less tightly compressed snow under the tires and that can make them more likely to slide in some situations.

Why not both? Both is good. But if you don't have AWD, yes, you definitely need winter tires.