There are exceptions for masquerade parties (cons, maybe?), parades and "those participating in the parades or exhibitions of minstrel troupes, circuses, sporting groups, mascots or other amusements or dramatic shows."
EDIT: a careful reading suggests that fursuits *within* con space would be OK - but not in an area not "wholly under the control" of the con, like the hotel lobby.
Just stepping out to the local park in a face-covering fursuit would be subject to fines or imprisonment. Kigurumi also might be covered, since they might be considered a fancy hoodie.
You can read the proposed bill here - http://webserver1.lsb.state.ok.us/