Problem is there are way too many variables in play under the conditions you are describing. This is why we need the car tricked out with sensors (and/or black box) that dealerships have access to.
What I can definitely say from experience is that it should not be clanging or banging. There will definitely be scritching and scratching noises. But things get complex as wheel weight and response changes due to the dynamic nature of snow. Snow packs into wheels, adding weight. Response changes based on how packed the road surface is. And you have 4 corners to deal with, so you are constantly applying/releasing the brakes. If everything (including the brake calipers) is not working smoothly, there will be sudden and loud noises upon engagement.
When you put on bigger & lighter wheels & wider tires, that does not make for good traction at all. Seen plenty of complaints on the Edge AWD even with the OEM 22" wheels, because they are so open-faced.
Aside from the things I have suggested to check, if you are not running dedicated winter tires, that might be something to look into and see it helps. I don't think it would tho.