They certainly don't fit well with either side of the conflict, though if you have to force them without a doubt the North:
1) They were anti-slavery, this alone with the slave vs anti-slavery territorial dispute alone is probably enough
2) Mormons were mostly a combination of two groups, the first being the older school Mormons who were from New England, especially around New York (picking up some people along the way of them having issues with the local, both native and White, and moving further west). So their closest cultural and blood ties were with the North. My wife was raised Mormon born in Utah from many generations of North, her and other Utah Mormons still form a major DNA match to New England.
3) The other group that made them up were recent immigrants into the US (mostly from Denmark, England, Scotland, etc) coming through the North. Certainly the North being the port of harbor for most and the immigration political aspects would greatly align them. Most of my wife's ancestry were European immigrants in the mid to late 1800s, some coming over during the Civil War and traveling straight west to Utah... the rest were older school Mormons from the North (one was pretty close to Joseph Smith, he managed his farm and his daughter was one of Joseph Smith's plural wives).
Those are some pretty key and strong ties to the North, most of which work equally as motivations against aligning with the South as well.
The only things I could think of that would tie them to the South would be a sympathy for being separate from the US Federal government since they were having major conflicts over polygamy as well as potentially keeping freedom for how they wanted to deal with local natives they were displacing (the US wasn't pro-Native in a general sense, but they still had a general policy and way of doing things and the Mormons never really wanted to follow any of that, waging their own wars with the Natives). Still even if they were not exactly pro US Federal government most of their political and blood ties would place them against the South in a general sense.