I would consider which channels I plan to receive. At my home, there are several VHF channels available, but only one UHF, so if I were selecting an antenna to take camping around here (Alberta) only VHF would be important. The site which Andy pointed to does mention that VHF and UHF are different frequency bands and thus use different antennas, and that a UHF antenna might be okay for the upper channels of VHF (7 through 13), but that would be easy to miss. That site is oriented to people trying to receive HDTV signals, most of which are UHF, so the UHF antennas get the most attention.
Before we put in a satellite receiver we just had an antenna for those local channels, and we use a VHF/UHF yagi designed like the
big dual-band yagi (from The Source), but more like the size of the same store's
smaller outdoor antenna. I can't imagine carrying anything this big on a trailer, so I would look for a smaller folding unit and settle for less performance. Mine at home is fixed in one direction which is a compromise between the local stations; at a previous home we had a powered rotater system to point the antenna at the desired station. On a trailer I would certainly use an omidirectional antenna (works equally poorly in all directions) or place a directional antenna where I could reach it to turn it by hand.
I see a lot less selection of antennas now than just a few years ago, as almost everyone has cable or satellite service - even in their RVs! It might be hard to find just the right unit, if looking for something other than RV models. 50 miles is a long stretch for a small antenna, and trying to pick up those weak signals with an omnidirectional unit with lots of amplification seems like a recipe for interference and noise. The greater radio experts can correct me if I am mistaken here.
One small antenna which seems to be widely
sold is Winegard's
Sensar III, which can be had with a manual folding and rotating system which apparently works from inside the trailer, from RV places like
Camping World. It doesn't look like it would be very sensitive, which is probably why it comes with an amplifier, but at least it would be directional to pick out medium-range signals. I haven't tried this type of unit.
Or just carry more DVDs...