Strange braking noise from low speeds, packing snow?

Recently I have spent a lot more time in bumper to bumper traffic. It seems like this problem only happens with harder stopping that you would find in stop and go- and usually from an initial speed of 10mph or less. If I have the ability to brake normally I typically do not experience this-

Anyway, when the problem does happen, it sounds like what can only be described as "packing snow". It is a low grumble from the passenger side wheel well/brake/tire area and it usually happens 2-3 times right before I come to a stop. It is not the abs system or anything like that- nor are there any dashboard indicator lights. The car also VERY SLIGHTLY lurches forward each time the grumble lets up.

Has anyone ever experienced this before? I am not sure if the car always did this or if it is something new.