Bear in mind that a smaller outdoor structure will not be as secure as a larger dwelling (and property insurance may not cover anything valuable in it, you should check). You will also need to keep it heated in winter, if you are anywhere it gets cold, or the equipment will suffer (from condensation, if nothing else).
I would not recommend working next to a rack of gear, it's noisy. There's a reason we have machine rooms and offices and they're not the same space.
So, what I suggest doing is to install insulation, heating, cooling, network cable, power, etc, as you have described. Then install whatever seating, desking, etc, that you might like. Then install basic networking gear (that you aren't going to be too upset with losing in case of a burglary). Then install a suitable display screen (when a 27" 4K display costs ~$600, perhaps you could cope with losing one to a burglary - depends how well off or how well insured you are, and what your local crime rate is). Use a laptop to compute with and take it indoors when you're not using it. Leave the rack of compute gear inside too, in a room you are not in most of the time. Don't leave any data storage out there, put that in your house also.
Obscure the windows in this outhouse while you are not using it; blinds, curtains, or shutters (locked or interior, so the burglar can't just open them and take a peek). Do not be seen loading the outhouse up with gear either, or someone may make a mental note and come back later, when you are out.
It sounds cool, but bear security in mind.