I don't know any specific event that would have caused the desertions [Certainly Lincoln's election had no impact on the men's decision to leave], but I do know that Hood's army was demoralized after the fall of Atlanta and many men could see no chance for success in his plan to go to Tennessee in hopes that he could reconnect with Lee's Army in Virginia. In every case the decision to go home was a personal decision and each man had to make it for himself.
Many men had seen enough war, lost enough brothers and messmates, marched and ditched enough to last a lifetime, eaten enough bad camp food, seen enough sickness, and certainly did not look forward to another winter without winter clothes, blankets, tents or a hope of any improvement in their situation.
Those who remained faced all of that for another two months. Many of them stayed and paid with their lives on the battlefields along the Western & Atlantic RR, at Florence, AL., crossing the the Duck river, Springhill, Columbus, Franklin or Nashville, TN. Some died in the northern prison camps and some in the rear guard actions as the army retreated to Alabama and Mississippi.
Certainly these men made a tough decision that they would live with for their lifetime and for some that lifetime was short.