A big part of antebellum American politics was ensuring that the admission of a new free state was balanced by theadmission of a new slave state. Lots of plans were floated for acquiring new lands that could become slave states, including purchasing Cuba. But eventually geography and climate would have left the Southern plantation economy with nowhere to expand to. Did Southern politicians have a plan in mind for this eventuality? Specifically, did the consider splitting an existing slave state in two, in order to get the extra senate seats?
Article 4, Section 3 of the Constitution is relevant here:
New States may be admitted by the Congress into this Union; but no new State shall be formed or erected within the Jurisdiction of any other State; nor any State be formed by the Junction of two or more States, or Parts of States, without the Consent of the Legislatures of the States concerned as well as of the Congress.
Throughout the antebellum period the House of Representatives did not favor the South in numbers, and much of the South's congressional power came from using the 50/50 split of the Senate to its advantage. Since the excerpt above refers simply to the "consent" of Congress, presumably the House would have had to pass any measure trying to split up states and that would have been a tremendous hurdle.
But, to my knowledge, no serious attempt to do this was ever made and I would argue that's because southern expansionists were too busy pursuing other avenues. One of these was expansion southward into the Caribbean, Central America or even South America. These discussions reached their height in the 1850s, especially as they became embroiled in the sectional issue of slavery rather than being purely about nationalist visions of Manifest Destiny and the spread of American styles of government. Cuba was a particularly coveted prize among expansionists mainly because of its perceived potential for slave institutions (as opposed to, say, Mexico).
Next, it was indeed widely believed that northern climates would be unsuitable for slavery but that didn't mean that Southerners ran out of western prospects for slavery's expansion before the Civil War. That's what the Kansas-Nebraska Act and later Bleeding Kansas was all about. While it's true that the South turned toward secession as they came to feel geograpically bottled in, this needs to be viewed the broader context of the communication breakdown and increasingly vicious political climate of the late 1850s.