YMMV, but I just saw this post on a local board:
"the access to the South Loop and Cathedral trail heads are chain-linked off from the picnic area entrance to the private property drive. Posted access is suppose to be from the Echo trail head...but there are shortcuts.
Snow on the trails is packed and crusty for the most part; watch your footing on old post-holes. Snowshoeing is good off-trail and across the chutes. Good pace can be made on the trails in boots; I used some Kahtoola Microspikes and they worked well, but not necessary; a few crust breakthroughs, but solid for the most part.
Ran into one other hiker, who was wearing shorts and approach (running) shoes. He had already summited Griffith Peak, and was on his way up Cathedral. The concern is that he was alone, traveling light, with no winter gear for an emergency overnight...a broken ankle up there could be disaster."
I don't know how far he went.