What could the problem be? Exposure to the elements just ain't the greatest thing from the electrics. First, battery terminal connectors will oxidize at a much faster rate. Oxidized connectors make for resistance to electrical flow, and that's a real problem when you're trying to charge your battery--you want the best flow possible.
But there's more: Road debris, tree leaves and needles, et al, can take up residence on the top of the battery. Add a little water and you have the makings for electrical current leakage. Yes, for real, a small amount of juice can begin to flow from the battery posts across the medium you're growing on the battery. Even small amounts can add up, reducing the available amount of juice for your use, and eventually killing off the battery.
So take the big plunge: Invest in a battery box to protect your leaded investment. For less than $15 a pop you too can liberate your 'lectrics from the fear of exposure.