speaking from experience - I would not cover it. My first trailer which I had someone build for me = I paid extra to have the floor insulated. He in turn covered it with a aluminum panel which looked good = and looked to be well sealed. In the second/third year I started getting what I thought to be was door/window leaks when driving in rain. Never was able to get the leaks to stop. In the 3rd year the vinyl floor covering bubbled up - I in turn removed it. Than the 4th year, the floor plywood bubbled up which is when I realized where the water could be coming from - ends up the builder had never sealed between the frame/body in front and over time, road debris/water from my PU had been pressuring in past this un-sealed area, thus filling up the insulated cavity created by the aluminum under panel. (the water would just stay inside pressuring up and soaking the floor from under = ending up rooting the whole floor out.) My replacement trailer since is open underneath with a good coating of the black stuff on it - road wash/debris just drops off when traveling and as far as ever needing a insulated floor? - with the 5/6in thick mattress = I don't think so........... after 5 years of this trailer = it is doing just fine!!!! (same brand of doors/windows as before = never have had any problems with leaks like I had 'thought' I had had before) But - hindsight being 20-20 - if I was to cover the underside ever again = I would put "drain" holes in it next time...............
PS = I live in the Pacific NW on the 'WET' (west) side of the Cascades = so yes, I am familiar with rain............as far as 'wind drag' goes, the air spoiler I built off the rear upper edge of my PU canopy has worked out well so far, after almost 20-thousand miles of use these last 3+ years = gaining over 1.4+ mpg overall average increase.......(not much better than 16.0mpg prior and now, minimum of 17.4+mpg consistently on long steady runs...)