Yes I have. In two different playthroughs. When I touch the gate for the first time. a cinematic starts, where the game goes to nightfall. However after that, the gate is not open. The prompt is still there, and I can press X how much I want, but the gate stays shut
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.