Split the nut to remove it. Probably by drilling a 1/4" or so hole in the nut parallel with the stud on one side or two opposite so it's weak enough to split with a cold chisel. Or you may have a nut splitter shaped such and strong enough to get in there and do the job.
Very unlikely that the stud is reusable.
Possible no damage was done to the hub, you won't know until you get it apart.

Replacement stud is likely available from NAPA or your favorite auto parts store. First try looking it up by application, then by dimensions if no luck by application.
Here's the original parts book page about hub studs and dimensions.
http://chevy.oldcarmanualproject.com/parts/1929_54/370.htm

The parts catalog will be your friend, introduce yourself.
http://chevy.oldcarmanualproject.com/parts/1929_54/index.htm

More good manuals and literature found here
http://chevy.oldcarmanualproject.com/

•1951 GMC 250 in the Project Journals
•1948 Chevrolet 6400 - Detroit Diesel 4-53T - Roadranger 10 speed overdrive - 4 wheel disc brakes
•1952 Chevrolet 3800 pickup
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"First, get a clear notion of what you desire to accomplish, and then in all probability you will succeed in doing it..." -Henry Maudslay-