JMO, but having owned 2 trailers with an enclosed underbelly and now our current trailer without I far prefer no underbelly. Access to anything when it's enclosed is a major PITA, when it's open you can run cables, hoses, etc, with no effort at all.
Open up an enclosed underbelly and you're sure to find wires and hoses run haphazardly all over the place, with little to secure them other than the underbelly itself. The few cables and hoses running along the underside of my current Coachmen are properly dressed and tied in place. As far as extreme cold or hot weather camping is concerned I haven't noticed any real difference at all between having an enclosed underbelly or not in temps between freezing and 100F. Claims that an enclosed underbelly makes for more efficient towing is just "sales speak" and offers no advantage at all.