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The Overlander is a wonderful trailer for long trips in comfort. I believe that by 1971 it was classed a 27' trailer; my '64 Overlander actually measures 26' 8" and was classed 26' by Airstream. When fully loaded for a vacation, my '64 Overlander weighs in at 6,000 pounds (a bit more or less depending upon duration of trip). The link below will take you to Airstream's web site where you can find information about the dry weights of Vintage Airstreams and their hitch height requirements.
Airstream Trailer Dry Weights and Hitch Heights
The thing to remember about dry weights is that they do not include any optional equipment nor do they include any fluids such as water or propane. In my case, the actual dry weight of my trailer is 4470 pounds (factory listing was 3930).
While I am not particularly familiar with Ford products, I suspect that the Overlander may be a bit large for your Ranger. The smallest tow vehicle that I have used to tow my Overlander was a '95 Chevrolet K1500 club cab pickup with 5.7 Liter V8 and 3.73 gearing - - it was fine in level territory but was overwhelmed when traveling in the Rocky Mountains (couldn't maintain more than 30 MPH when pulling the I-70 grade near Eisenhower tunnel - - an experience that I never wish to repeat).
Doing a thorough checkout of all systems in below freezing weather will be difficult, and at least as far as the water system is concerned probably impossible. So far as the water system is concerned, you will want to do a thorough visual inspection looking for evidence of leaks (staining on the floor or deposits on the pipes). Examine the water heater looking for signs of rust or any other type of corrossion. You will want to be sure that there is a water pump present and that it is connected to the water storage tank. The refrigerator is one appliance that should be such that it could be demonstrated - - it is also among the most expensive appliances to replace if it isn't operational - - my new Dometic was nearly $1,200 with professional installation. The furnace should also be such that it could be demonstrated - - a profesional replacement of the furnace in my coach was just under $600. If there is a roof air conditioner, it will obviously be too cold for the compressor to kick in, but the fan should run and circulate the air. The owner has probably stored the battery so you will likely be looking for the presence of a Univolt or power converter and for functioning of lights and other electric appliances. You will also want to note any soft spots in the floor or other evidence of water damage - - the two spots where I have had leaks in my Overlander were around the refrigerator vent and in the rear one-stop service compartment around plumbing vents and rear marker lights.
In all reality, even if the appliances are currently operational you may be looking at replacements in the not too distant future. When I purchased my Overlander in '95 all of the appliances were original - - but failed, one-by-one until all had been replaced by 2000. The refrigerator was first to go followed by the furnace, the water heater, the air conditioner, the water pump, the Univolt, and the electic service panel.
You will want to provide yourself a cushion in negotiations to allow for new tires if the owner can't establish that the age of the tires is less than 5 years and that the tires are properly rated ST tires. It has been my experience that you can anticipate the need to have the bearings serviced, and often some brake work. In the case of my Overlander, a set of four new tires ran about $375 for Good Year Marathon ST load range D tires; and a complete brake overhaul utilizing fully loaded backing plates and freshly machines drums and shoes ran about $750. The DuraTorque axles also probably bear checking as well as they seem to be one of the most often mentioned items in discussion recently about replacement issues, and you have undoubtedly run across several threads about this issue - - it is the one area that still needs attention on my '64.
You will also want to check the propane tanks to see if they have been upgraded to the new standard OPD valves. If this upgrade hasn't been done, you may have difficulty filling the tanks in some parts of the country. To learn more about the OPD valve issue, check out the following:
WBCCI Article on OPD Valves and Aluminum Tanks
Upgrading the tanks to new valves isn't particularly expensive, and typically runs under $100 for a pair of tanks. If the tanks are steel rather than aluminum it may actually be cheaper to purchase new steel tanks - - or it might be an opportunity to upgrade to aluminum tanks.
Good luck with your inspection!