I don't know that I can give any specific ideas here, but refrigeration is sort of a neat topic.
The problem with refrigeration is that it is unnatural.
Energy wants to flow from where it is most concentrated to where it is least concentrated. That means everything cold warms up and everything warm cools down.
I can make things hot by releasing stored energy in a small area, but to make things cold I have to remove energy and that is tricky.
The easy way is to find something that is already (still) cold and use that. This is what a cold spring or ice houses would give you. This works great if you have something that is already cold and if it is cold enough for what you want to do. If you want something at 40 degrees and your spring is at 50 degrees, this isn't going to work. Also, once your cold thing warms up, it is over. You need another cold thing.
The next most method is evaporation. Liquid water will evaporate. Evaporation takes energy. The energy has to come from somewhere so it comes from the liquid water and whatever it is touching. How much energy it removes depends on how much water you are evaporating. How much water you can evaporate depends on the surface area of the water and the humidity of the air. Since the air can only hold so much water the closer it is to "full" (100% humidity) the less water you will evaporate. This make evaporative coolers work well in dry environments like deserts, but no so well in wet environments such as the coast. An evaporative cooler can not get any colder than the dew point of the air. This means that in the Northeast in July, don't expect to get lower than the mid 60s or so.
Now we get to chemical cooling. When mixed with water some chemicals will become colder than their surroundings. Ammonium Nitrate (NH4NO3) is the most common. When dissolved in water it gets quite cold. The problem is this is a one shot trick. Once the Ammonium Nitrate is dissolved in water it has done all it will do for cooling.
Now we have mechanical cooling. This is what the A/C in your car or house and your refrigerator use. If you compress a gas it gets hot. If you let a gas expand it will get cooler. So, if you compress a gas, keep it compressed and let it cool back to ambient temperatures, then let it expand, it will end up cooler than ambient. In practice there are some phase changes in there too, but you get the idea.
The propane powered refrigerator is a strange beast. It is part evaporative, part mechanical, and part chemical cooler that continuously recycles itself. Inside you have ammonia dissolved in water. The water is heated until the ammonia boils out. The now ammonia free water goes one way inside the unit while the ammonia gas goes another. The hot ammonia gas goes through pipes to cool, then is allowed to expand through a nozzle. This make the ammonia cool enough to become a liquid. The liquid extracts heat from inside the refrigerator to boil back to a gas. The gas is then adsorbed by the ammonia free water we made back in the first step, making room for more ammonia gas to boil off. The ammonia water is now heated again to drive off the ammonia, etc.
If you are trying to keep just a few vials of insulin cold, might I suggest some tests with simple thermos bottles. An icepack (instant or otherwise) tucked into a good stainless steel vacuum bottle with the insulin vials in the center might last a surprisingly long time especially if you take other measures to keep the thermos itself cool.
I don't know how well this would work, but if an instant ice pack in a thermos was able to keep the required temperature for let's say two days then 180 packs would buy you a year. At a dollar a pack (u-line, other on-line retailers) that is still only $180 per year.