No. There are OTA (Over The Air) DVRs. Here is an example of one. Not all the reviews on this one are very positive. And, I'm sure you need to have the TV scheduling information from another source e.g. Yahoo TV website. This is less convenient then a cable/DSL/satellite DVR with built in schedules and more like the old-fashioned VCR programming where you had to know the channel and start and end times to record.

Because the TV signal is weaker, and digital reception is binary :) (you either get it or not) with perhaps pixilated or frozen pictures a directional Yagi antenna would make sense. You can check out how your location fares at TV Fool. If TV stations are all over the map you need a rotor for the antenna. If the stations are all from the same direction, you can skip the rotor. You may want a signal strength meter for aiming the antenna and possibly and signal amplifier. Winegard makes some decent gear. You do have the advantage of being in a fixed location.

I came close to buying a OTA DVR while wintering in our motor home in Florida. The wife did not want to miss Downton Abbey and missed other activities at the campground. Also, because my motor home's HDTV does not have a strength meter, I'm probably going to buy this. Finding a distant station is sometimes a real PITA.

This does not address the cable channels that are only on cable.

Rayzar Automatic. Nothing particularly magic about it being for an RV other than it runs off 12 Volts (i.e. "house" battery). I'm not sure what the effective range of the antenna is.

What I mean by pricey is here.