It varied, both by region and depending on what stage of the war you're looking at. As you probably know, Lincoln repeatedly denied that he was going to war over the issue of slavery when hostilities broke out in 1861, and his administration actually supported a very conservative policy on this matter well into 1862. It wasn't until his release of the Emancipation Proclamation (which didn't go into effect until Jan. 1st, 1863) that the war became as much about slavery as the preservation of the Union. Doris Kearns Goodwin's 'Team of Rivals' spends a great deal of time examining Lincoln's personal view of slavery on a social, moral, and political level before and during his presidency. What you find when reading Goodwin's book is that Lincoln seemed to form fairly strong opinions against slavery early in his life, but until late-1862, he didn't feel comfortable risking his own political career, and later, the delicate political balancing act of his administration, to directly strike against it. There was a lot of concern that border states like Missouri and Kentucky would tip into the Confederacy if Lincoln backed emancipation initiatives, and even more concern that there would be a wave of political reverses (governorships, House, and Senate seats), and military desertions in established Union pockets if he acted.

I bring all of this up to illustrate that there was a fluid, complex tapestry of personalities and viewpoints in the north, and again, depending on the region and time period (1861 was a very different time than 1864, for example), it is hard to nail down any one consensus on the matter. To illustrate, there was one Indiana regiment that famously declared that they would rather lie down and let moss grow on their backs than fight for African Americans' right to be free. On the other hand, Massachusetts, long a hotbed of abolitionist activity and support, demonstrated an overwhelming willingness to volunteer troops throughout the war.

So, td;lr - it really depended. Throughout the war, attitudes and policies regarding African Americans changed, as did the opinions and actions of soldiers. Depending on where a soldier was from, where they were stationed, and the year we're talking about, it really varied. I think the real indicator is the fact that Lincoln was elected to a second term AFTER he had issued the Emancipation Proclamation, and the Union troops that voted overwhelmingly supported Lincoln over their former commander, the Democratic opponent in the '64 presidential race, George McClellan. Obviously, Lincoln had the support of the troops, and while this may not have been explicitly because of what he did to free the slaves in the south, they certainly didn't feel strongly enough against the initiative to unseat him as their Commander-in-Chief.

[Sources - Doris Kearns Goodwin, 'Team of Rivals'; Bruce Catton, 'Glory Road'; Jay Winik, 'April, 1865'; James McPherson, 'Battle Cry of Freedom']