I dont hunt archery, but hunt the late muzzle loader seasons sometimes clear till mid of January.
I've had excellent results using cow calls to call in elk in december and january. Not real big bulls mind you, but spikes, raghorns and cows. I've called several spikes away from herds of cows, and a spike or raghorn spotted alone at distance can usualy be brought to within 15 yards or so very easily with a cow call.
One thing I dont do, maybe this played in with the above "elk bailed at my call", is call to elk, especialy groups of cows in a situation where the elk should be able to see the calling elk. My experience with groups of cows has bean that if you call when they are out in the open, and they cant see the elk calling, they will bail. The use of a decoy may help this, but I havent tried. Cows in the reprod seem pretty easy to call to, but they may just respond and expect you to come to them, rather than they go to you.