I have lots of experience with walnut. I have used it for building tables, chairs and a really elaborate sitting system for a doctor locally.
I love working with walnut. I cut it and mill it whenever I can get the chance!
It would make awesome treads with some drawbacks. First of all, Slippage. I don't care what you finish it with, short of non-skid surfacing, those will be slick! I am sure you don't want shoes ...ie high heels etc walking on those nice surfaces, so socks and bare feet is it! Trust me when I tell you it's probably not your best choice for a tread alone
As far as fastening them down, I would slot cut the holes for movement and use tslot bolts, then fill the holes with plugs. I don't care how you cut or dry the wood you MUST allow for movement!! Quartersawn wood be best, with riftsawn next best. Keep in mind Walnut doesn't fleck or Ray like White oak and such, so your really doing it for dimensional stability and unless these are big sticks its probably not worth the effort. Of course you could still put the wood in and apply carpet runners to each one for fall protection and noise reduction.
Hope that helps!
~Dave