If I recall properly, the Whites in the Confederacy were not allowed to vote. From the perspective of these people, Lincoln had not only destroyed their lands, homes and killed their people, he had evaporated their capital, their industry, and now intended to put their former slaves above them as their masters by giving them the vote which they no longer had.
In fact, several majority black legislatures were created by this method, but it's hard to find any references to this anymore. Because it became embarrassing to the Union, they quickly undid it. The references to these events appear to be nearly scrubbed off the internet. I haven't found a source for this (for how embarrassing were the doings of these legislatures for the Union officials running the South at that time.) for a long time, but I recall reading it in several history books decades ago.
Are you suggesting that Lincoln is publicly suggesting that some former slaves should have the franchise, ...
Actually I thought he went about it in the most reasonable manner possible. His suggestion that it be "conferred on the very intelligent, and on those who serve our cause as soldiers." is as good a way as any to attempt selling this idea politically, but no matter what he did, the idea would not be welcomed at that time in the South.
...while privately suggesting that they be sent to colonies?
So far as sending them to the colonies, he had proposed that they be hired by the Federal Government to build a Canal across Panama, and once they were settled in Panama, they could send for their wives and families. That was his Panama plan. He was trying for inducement at this point in time. (1863 I think) He had been pushing various "Get them out of America" plans since the 1840s, I think.
Regardless, this is an idea that obviously intrigued Lincoln at one point. It would not shock me if he had explored it again in his second term. But, as others have pointed out, participation would have been voluntary, and it likely would have gone nowhere again.
I think a voluntary plan would have gone nowhere again. Yes, I think that's correct. The point in bringing it up at all is to demonstrate that Lincoln didn't believe the "all men are created equal" anymore than did the founders four score and seven years earlier.
How did Lincoln feel about the enslavement of the black man by the white man?
Here, again, Sir, you are mixing your mythos or outright lying. Lincoln had his own "Central America plan" which he personally laid before a delegation of leading blacks. It had nothing to do with building a canal, but had more to do with coal. Herein, you are referring to the very dubious Panama Plan of Gen Butler (the canal plan, that Butler claims to have introduced to Lincoln in April, 1865). Only Butler is the source for this Panama plan. Two entirely separate plans which you have just mashed together. Just trying to be objective.
Here is an excellent summary of Lincoln's colonization plans & actions.
The first point everybody needs to put firmly in mind is that colonization of freedmen was official US Federal government policy, proposed by Thomas Jefferson and supported by congressional acts & funds since 1819.
In 1819 Congress voted $100,000 for colonization of freedmen, a number corresponding today to around $100 million -- enough to get started.
As a result, about 13,000 African-American freedmen settled in Liberia over a period of 40 years.
In other words, a drop in the bucket.
In 1862, at President Lincoln's request Congress again voted money for colonization, this time $600,000 and again about 14,000 blacks signed up, volunteered, this time for an island off Haiti.
But only a few hundred were actually transported and most returned in 1864 when the experiment failed.
Point is this: since Jefferson, colonization was a permanent fixture in all plans for peaceful abolition, to which Lincoln subscribed.
But Lincoln's ideas were always voluntary and after several failures he gave up on them.
Congress also gave up, in July 1864 withdrawing its authorization of $600,000 for colonization.
Of the $600,000 originally appropriated, Lincoln had spent only $38,000 and had clearly long given up on the idea.
So, even if General Butler's account of his meeting with Lincoln in early 1865 can be credited (I don't think it can), but even if, it represents nothing more than casual conversation, not government policy backed by congressional authorization & funding.
All of that was withdrawn, with Lincoln's approval, in July 1864.