I think I have to agree with the verdict given by many above: that he seems to have been a deeply "spiritual" man without any interest in or affiliation with any "organised religion."
Nonetheless, I am not convinced that his belief in the transcendence of God's will beyond the knowledge of mankind is necessarily a sign of agnosticism - such a belief could just as plausibly be a product of a personal reverence for God, and an unwillingness to see him appropriated for political purposes (like Mandela in South Africa), rather than of categorical disbelief in Him. After all, a devout theist could just as easily believe in the same "distance" between the human and divine wills as an agnostic, and hence, Lincoln's expression of such a "distance" is not in itself terribly revealing. Additionally, the Christian-ite culture and context of his time empowered the Bible with an ability to serve as a medium through which to effectively communicate across different social demographics, meaning (as many have identified above) that Lincoln's quoting of scripture in itself is not indicative of his personal spirituality, but is rather a reflection of the society with which he sought to engage.
Of particular relevance to this discussion, which I have pondered frequently, is his second inaugural address, which not only adopts a sermon-like tone, but also explores the ethics of a just war from a Christian perspective, which seems distinctive in its themes and language from his earlier theological expressions. I feel that retrospective discussion all too frequently conflate the different phases and maturities of an individual's life, and can easily blur the evolution and maturity of their thoughts and beliefs. This is why I think that all of his religious statements should be interpreted in the context of each other, and that neither his early stated disagreements with the church, nor his later avowal of Christian-like principles, should be the sole lenses through which the views of his life should be interpreted. Instead, I see a trend across the evolution of his statements over time which seem to indicate the thawing of his attitudes towards religion, to the point where the religious views of the 1830's Lincoln seem markedly different to those of the 1860's Lincoln. As cross-sections revealing the intricate consciousness of a complicated man, these statements we have been able to glean from the fabric of history serve as valuable reference points in tracing his theological evolution away from agnosticism to deism. Even though they do not testify to a man who has accepted Jesus as his personal Lord and Saviour, the subtle nuances that exist demonstrate, in my opinion, his evolution away from agnosticism and to an "understanding," if not wholehearted acceptance, of Christianity.
(Additionally, Lincoln's "martyrdom" and elevation to the position of a secular saint has politicised his personal faith in a way that makes his views a highly contested battleground for those who seek to appropriate his legacy for their own particular agendas, a contest which existed in the aftermath of his assassination, and I believe, has contaminated whatever accuracy may have existed in the sources beyond remedy. Besides, at the end of the day, a person's views are theirs alone, and can never be known by another with complete certainty.)