This state's classification carries no date range for the species.
American woodcock does not appear anywhere in WGFD Chapter 14 (migratory game bird regulation) - confirmed by reading the full 12-page regulation, not just a keyword search. Its core range is eastern/central North America; it is documented only as an occasional vagrant this far west (including western Wyoming per rare-bird records), not an established/huntable population. No open or closed season exists to report.