Solar Panel with Deep Cycle Battery for winter storage

I have a cheap solar on my vechile battery which stays in and is in working order when spring comes. I have no load on the rv battery and its junkville in the spring. I know the better solar is putting out more voltage and it has its own shutoff installed in it. So I may have to assume that the new rv battery was******to start with... But any who... Theologically I should be able to leave a deep cycle battery on the solar over the winter months?