yeah that's how it works, it restricts you from going into Cathedral Ward since it was cut.
you backtrack, then find an opened door (check the central yharnam lantern) then continue from there.
if you want to kill the winter lantern, bait it to the "objects that can be cut", and make it fall onto her. the location is the opened door, you may get a clue what's the "object that can be cut to make it fall" there, not gonna give spoilers.