I've heard that statement made a couple of times now, but having read almost all of Lincoln's works, including letters and other correspondence, I feel pretty confident in saying that it's just not true. By most accounts he was happily married. C. A. Tripp wrote the most famous book on the matter, but most historians will tell you that Tripp was just reaching for a controversial theory and that his arguments are really weak. A lot of the speculation comes from the fact that he lived with other men at certain points and even shared beds with them, but that was a really common practice at the time, mostly just because it was practical and even in some cases a necessity for poor bachelors who couldn't afford their own bedrooms. Lincoln also never tried to hide the fact that he did share beds with other men, and brought it up himself a couple of times. If he had ever shared a relationship with any of those men, they would have had plenty of chances to admit to it. Tripp actually claimed to have found the diary of one of Lincoln's old friends who he had lived with that said they had been in a relationship, but it was basically written off right away as a fraud.

Funnily enough, a poem written by Lincoln that started a lot of the speculation about his sexuality was actually published in Herndon's bio of Lincoln, the same disputed source that the original post came from. That's of no real significance, just a fun coincidence.

TL;DR - Nah, Lincoln was definitely strange and people like to theorize, but he was heterosexual.