Hi blackriderx,
Wool certainly isn’t mandatory although it’s a great temperature regulator and it can also be used to pass the fire regulations instead of using a different type of barrier so they are also a very popular choice for those that prefer more natural materials in their mattress. It is also more resilient than many other types of natural fibers. As far as comfort or performance vs other materials this would be a preference choice. There is more about the pros and cons of wool quilting vs an unquilted stretch knit cover in post #6 here.
Several of the members in the online list have latex mattresses that either come without a wool quilted cover or can replace the regular wool quilted cover with a stretch knit cover. These would normally use a different fire barrier such as rayon/silica and with a prescription some manufacturers can make a mattress with no fire barrier at all (see post #2 here for more about fire barriers). Some manufacturers such as Sleep Essentials only sell their mattresses by prescription.
There are many variables in a mattress that can affect sleeping temperature (see post #2 here) so how a latex mattress would compare to your innerspring mattress in terms of temperature would depend on the type of materials and components that are above your innerspring. Latex is generally the most breathable of all the foam materials (memory foam, polyfoam, latex foam).
Futons have come a long way since the days when they were mostly made with cotton and there is a much finer dividing line between some futons and some mattresses. There are some good options for futons in post #2 here that can give you a sense of the types of futons that are now available if you do decide to go in that direction.
There are also some manufacturers that make traditional innerspring/cotton mattresses as well. In most areas of the country these are more difficult to find but in the general NYC area there are several places that carry these including …
Charles H. Beckley, Inc. (with 15" dacron fiber)
Naturepedic
http://www.thecleanbedroom.com/Organic_Mattresses/Cotton_Innerspring/Royal_Organics_Organic_Cotton_Mattress.htm (Doctors prescription required)
whitelotus.net/organic-cotton-latex-mattress-rx-required.html also makes a latex/cotton mattress/futon as well but you need a prescription because there is no fire barrier.
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Phoenix