We've had both enclosed and open underbellies. I installed 100% electric heating in our current TT and we no longer use the furnace and therefore no warm is blown into the underbelly. We camp down into the 30s but never in freezing temps. When the underbelly isn't insulated or enclosed/warmed, the floor will feel quite cold on your feet and your legs will also feel cold. Uncomfortably so to us and we're not even in sub-freezing temps. We use slippers or heavy socks and when watching TV use a blanket on our legs.
Insulation will definitely help and will reduce stratification, the temp. difference between floor & ceiling and improve interior comfort. I'd also through the trailer and seal up all cracks and gaps you can find in the floor. But you'll still need to vent the interior to remove moisture laden air - a dehumidifier could be an alternative but not without power of course. Resist the temptation to insulate and seal the heck out of it and not vent it otherwise you may end with rot, mold & delamination.
Use a closed cell rigid foam blanket around the tanks and everywhere else you can fit it in and then spray foam in a can to fill cracks 'n gaps. You may want to relocate piping to the underside of the floor as needed so it is on the warm side of the insulation. Note that batt insulation absorbs moisture and when it does, the R-value can drop significantly. It's also not a good choice in RVs but is simply cheaper to install.
