The temporary traffic order for the closure doesn’t cover the whole of Snake Pass, only about 200m of road. There is no trespass unless on the bit they are working on. A number rode up from Glossop side yesterday.
Back on Mam Tor topic. You can ride all the way up on mtn bike. Least you could about 5 years ago when I last did it. Road bike you’d almost certainly need to walk sections unless you has skills…