Come July buy a leftover reduced price cow/calf elk tag. No draw needed. Non-resident price with conservation stamp should be around $250. The season (at least in years past) varies but is usually around Oct 1 to Dec 14, with a break the last two weeks of Nov (I have no idea why). Some areas are open till Jan 31.

I killed this cow off Commissary Ridge (unit 102) last Nov, though she was several miles in. Come the two weeks the season is open in Dec, the elk should be much closer to roads, or earlier if snow comes earlier. Ya gotta be careful though, as even the main roads don't get plowed. Lots of elk in that area, and it sucks killing a cow when she is in a herd of about 200 with several good bulls mixed in. Ya gotta do what ya gotta do though. There's a lot of good bulls around there, but like said, you missed the draw.
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The fishing around there is good too. Just don't let all the rutting mulies distract you in Nov.