I find myself in a part of the US (NY Adirondacks) where travelling anywhere requires a vehicle of some kind and yet it is prohibitively expensive to buy, register, insure and maintain a vehicle and get a drivers license. My question is that if I can't use a vehicle (car, truck, and/or the like), what can I use to get around where walking or biking is not a viable nor practical solution? Before it is mentioned there is no public transit of any kind and the distances are at least 30 minutes or more by car.
All-terrain vehicles (aka four-wheelers) aren't allowed on public streets and highways (with rare exceptions). And they still have to be registered and insured (unless you operate it exclusively on private land).
There is a special registration class for agricultural and farm vehicles such as tractors, but it is only allowed if you actually have a farm. You are only allowed to operate them on public roads along approved routes (e.g. between two fields of your farm). They also have to be registered and insured. It doesn't say so explicitly there, but I think a driver's license would be required too; possibly an even more expensive commercial driver's license.
Riding mowers are probably not "street legal" as they will not have all the required safety equipment. You might get away with driving one a few hundred yards along a street between fields, but not more.
(Not relevant for this site, but there are clear practical and safety problems also. These vehicles are all very slow; if a trip takes 30 minutes by car, it will take hours by tractor. Their slow speed, small size, and lack of safety features will also make them very dangerous to drive in traffic. If you want to know about possible ways to arrange your budget to afford safe and legal transportation, head over to http://money.stackexchange.com.)