It is often pointed out that McClellan repudiated the "peace plank" of the Democratic platform, promising to win the war no matter what his party's official position was. However, it is worth pointing out that he released this statement only after The Battle of Mobile Bay and the fall of Atlanta had made it clear that victory was within the Union's grasp. The very fact that McClellan wins the election ITTL indicates that the Confederacy has been more successful on the battlefield in 1864 than was the case IOTL. In such a scenario, would McClellan have maintained a pro-war position? Maybe. . . but maybe not.
McClellan had already shown a willingness to deal with the Copperheads. He publicly endorsed the Copperhead candidate in the 1863 Pennsylvania gubernatorial election, George Woodward. Before news of the fall of Atlanta, McClellan's advisors and friends told Democratic newspaper editors such as Manton Marble and others throughout the 1864 campaign that McClellan was committed to end the war through negotiation rather than force.
All of this clearly indicates that McClellan was hedging his bets. Had the Confederacy ended 1864 in a more or less stable military position (i.e. Grant stopped in Virginia, Sherman stopped in Georgia, and the Shenandoah still in rebel hands) it seems likely that McClellan would have been willing to enter into a cease-fire and negotiations with the South.
Now, McClellan would have sincerely desired that these negotiations lead to reunion (as was the case with most of the Peace Democrats, even Clement Vallandigham) and was willing to abandon the Emancipation Proclamation in order to achieve this. But this was a delusion. Jefferson Davis would never have been willing to give up independence under any circumstances, slavery or no slavery, so the negotiations obviously would have failed.
The problem for the Union would have been that, having halted the fighting, it would have been politically impossible to resume hostilities. A large portion of the Republican Party would essentially abandon the fight, since they would no longer have considered the war worth fighting if the abolition of slavery had been dropped as a Union war aim. And with the fighting stopped for at least a few months, morale in the Union forces would have plunged. Desertion would have become much more common. Recruitment would have become much more difficult and resistance to conscription would have become much stronger. The South, meanwhile, would have been greatly strengthened by the cease-fire, the military pressure erased and their financial problems eased. A cease-fire might even have lead Britain and France to finally go forward with their oft-suggested plan to offer mediation of the conflict.
Regarding the argument that Lincoln would have pressed forward with the war between early November and early March, the question is. . . how? The campaign season was at an end and the onset of winter would prevent any major Union offensive. As already pointed out, the very fact that McClellan won the election ITTL indicates that the Confederacy ended 1864 in a much better military position than was the case IOTL, suggesting that any Union offensive during the winter of 64-65 would have easily failed.