There is a lot of information missing to give you a good answer.
1) Are you with any insulation in this shed?
2) How far from where you can park your vehicle?
3) Is the ceiling finished and around 8 ft high?
4) For A/C will you have a generator powerful enough to run an easy start 5 to 8k BTU unit?
5) How remote is this facility and can anyone watch it from another full time home?
This leaves me answering in the abstract.
But If it is quite remote I'd not install anything in it that would entice squatters to occupy it
when you aren't around or steal your equipment.
If you don't have to pack equipment a great distance from your vehicle there some light
weight solutions for heat.
These propane catalytic heaters by Coleman are around used. These run 2 to 4K BTU.
If your cabin is 12 X 16 X 8 that's roughly a bit over 1500 cubic ft of area to heat. So you could go from 2K BTU up to 8K BTU. You could take these home with you when you leave. Propane may be
brought in in a couple of 20lb BBQ tanks depending on how long you intend to stay. These types of heaters are known to produce little or no carbon monoxide. (popular with RV'ers for that reason)
As for A/C the Fridigaire easy start 6K BTU window unit gets very good reviews and could handle the sq ft of floor you have.
As for matching a generator to an AC unit check out this link:
https://www.howtolookatahouse.com/Bl...generator.html
But this equipment will have some weight and I doubt you will want to leave it unattended if you are only there occasionally.
Lastly, refrigeration. You can find propane absorption refrigerators from wrecked RV's. They aren't that difficult to set up. But they must be installed on a "LEVEL" base
Visone RV com in Kentucky is one RV wrecking yard I know of where you could get a used fridge.
606 843 9889 They are a huge operation.
If you have time to look around both on the net & real world you may find this stuff at a reasonable price. These heaters don't weigh that much but a couple of full propane tanks will. The AC unit will weigh a bit and the generator likely weigh plenty. You may need to get your vehicle as close to the cabin as possible for AC.
This is the best I can offer you with the info provided.