First of all, not all Walk-in areas allow deer hunting. Walk-in areas are private land that the G&F has entered into an agreement with the land owner to allow public hunting. The land owner dictates what can be hunted, within G&F regulations. Has to be the right season and all.
Besides walk-in areas, there are also Hunter Management areas, Wildlife habitat management areas, and others can be found in the Wyo. G&F site:
http://gf.state.wy.us/index.asp
Click the link on the left "Public Access". There you go to walk-in areas, Click Johnson County (or wherever), and see what is available for deer. (Hunt area #, dates, rules of landowner, etc.) Also check out "Wyoming G&F Facilities & Access info on the same page. On the right you'll see a link saying "clickable map". Click "NE". See if any of those allow deer hunting.
Keep in mind that a good BLM map of the area will show you all the public land in that area like state land, blm, and Nat'l Forrest.