IIRC, you will just end up spending more, as they cost more to make to withstand deep cycle use. They have a larger number of thinner plates, or something like that. A starting battery will have a much shorter life if it is frequently discharged too much between chargings, but I don't think it would hurt a deep cycle to use it in a starting application. It wouldn't surprise me if deep cycle batteries worked better in very cold climates, but probably are overkill in moderate climates.
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Looked up a couple things, got most of it backwards. Starting batts have lots of thin plates for maximum cranking amps, but will be damaged by deep discharge. Deep cycles have a smaller number of thicker plates, which are more durable, but may not be able deliver the cranking power of a comparable sized starting battery..