Deep question for YA R+S, and the above poster (thanks for the links) is right about how sadly few know who this man was. And his theology does take some sifting thru, and while i am by no means an expert on him, it is evident that the man loved and sought to defend God's holiness and justice deeply (his conversion was deep), while seeking to make sinners ware of their need for mercy.
Finney did not deny the atonement, which despite the agreement of the Biblical necessity and reality of it, is often misunderstood today, and even though with a basically sound view of it can use more understanding on the matter.
Finney rightly denied that Jesus suffered all that man would have suffered in Hell fire, but that it was the fulfillment of the Mosiac law of atonement, in which the most precious thing (innocent blood) became the acceptable offering that enabled forgiveness.
In his own words stated,
"The sacrifice made on Calvary is to be understood as God's offering to public justice--God himself giving up his Son to death, and this Son pouring forth his life's blood in expiation for sin--thus throwing open the folding gates of mercy to a sinning, lost race. This must be regarded as manifesting his love to sinners. This is God's ransom provided for them. Look at the state of the case. The supreme Law-Giver, and indeed the government of the universe, had been scouted by rebellion;--of course there can be no pardon till this dishonor done to God and his law is thoroughly washed away. This is done by God's free-will offering of his own Son for these great sins."
(1 John 4:10) "Herein is love, not that we loved God, but that he loved us, and sent his Son to be the propitiation for our sins."
It appears however, that Finney may have been in error regarding the means of justification, if what men like Horton says is true, however having read Finney saying things that in context refute some of the things i have seen him charged with, it appears Finney's theology was not always consistent, or that his adversaries, are selectively taking quotes out of context or as definitive of him when they are not. I think some of what he wrote, which led to charges of teaching salvation by works, must be understood in it's context, of a reaction against extreme Calvinism which produced passivity and a fatalism in the light the Sovereignty of God.
And if i may take space on this (you are likely to have few responses to our question), i would like to say that some things i must Scripturally disagree with Horton about is that of blaming Finney's use of "new measure" for the kind of superficial conversions we see under modern Revivalism. For using measures (altar calls, mourners benches, etc.) that are practical to Biblical ends certainly have Scriptural precedent (Mark 6:39; Lk. 4:3), and Finney's preaching was not that of easy believism, as can be seen by reading some of his messages today, but that which often produced the kind of conviction that made measures necessary to deal with souls in distress of conscience. But as in the case of the O.T. offerings, things that are used of God can end up being institutionalized, and the "altar call" has become much a perfunctory if something useful practice. While the weak preaching and lack of conscience today is to blame on superficial conversions. Yet institutionalized is what many of those which criticize evangelical churches are, which often are those who cannot see clear enough as to abandon paedo baptism as well as the requirement of static liturgies and liturgical seasons after the manner of Rome.
Much is laid by Horton upon Finney's rejection of original sin, yet he would be right in rejecting the idea that infants are culpable of Adam's trangressin, unless it can be shown that in some mystical way we are, however, while we realize effects, good and bad, of our father's decisions, and suffer the effects of Adam's fall, the justice of God forbids actually punishing the child for their fathers sins (Dt. 24:16; Ezek. 18:20), and the final judgment is "according to their works" (Rev. 20:12, 13) - not someone else's.
I assume Finney would also deny limited atonement, as i think we should, as it is no fault of God that those who are invited to a prepared feast refuse to come (Mt. 22:1-7), and it is unwarranted to read "the elect" into the inclusive statements the Scriptures make about the scope of the atonement and offer of salvation.
(1 John 2:2) "And he is the propitiation for our sins: and not for ours only, but also for the sins of the whole world."
(1 Tim 2:4) "Who will have all men to be saved, and to come unto the knowledge of the truth."
(2 Pet 3:9) "The Lord is not slack concerning his promise, as some men count slackness; but is longsuffering to us-ward, not willing that any should perish, but that all should come to repentance."