Hi,
I am a horse person and have bought many, many tons of hay over my life. Have seen pretty much every type of set up, from small squares to large rounds and large squares.
1. You don't want any more condensation on hay than you have to have. That said, yes there are folks who leave their large rounds in the fields. Who buys that? Cattle folks primarily in my area. Horse people mostly won't touch it if it isn't in a shelter as mold = colic = large, large vet bills.
2. If a person goes to all that trouble to put their hay (any hay) under a shelter, most will put it at least 3" inches away from a wall, most I have seen do at least 4-6". It keeps water from dripping into the hay and causing mold. Also reduces fire hazards as wet hay can spontaneously combust (especially those small squares!). So most have some air space around it.
If I were you and you wanted to rent the shelter to a local farmer, I would first find out what the intent is. Is the farmer going to sell the hay commercially? i.e. are you going to have random people driving up to buy hay? Or is he going to store his OWN hay there? If it is his own hay, I would be far more willing to rent the shed.
You would probably do well to call a trusted friend who is farming and get their advice..preferably someone who bales and sells/stores hay. If you can't find one of those, then ask your local feed store or co-op. The one your DH dealt with would be best and ask their advise concerning what type of "tenant" you could get for the least amount of "trouble". One thing I think would likely be a good option is to find a farmer/horse person who wants to lease the shed to store equipment in.
That is low risk, low intrusion on YOUR time/land. A farmer who has a large combine/tractor/hay baler, etc. might rent it for less than one that is selling hay, but you won't be dealing with random people. A horse person might rent the shed to store their huge living quarters horse trailer in to keep it out of the sun. Might have to deal with them weekly, but as long as they pay, they wouldn't be bringing random folks on your property.
Good luck, and you can do this, just be careful who you deal with, get references and ask for deposit, first and last months rent.
and get EVERYTHING in writing!!! Use a local attorney and make sure it is all legal and you are protected. I cannot stress that enough! (oh and check with your insurance, many will not cover a "commercial" operation and may consider leasing the shed as "commercial" use. Farm Bureau has a heap more sense than many when it comes to things like that, so be sure to check in advance!
(oh and you might make the renter take out insurance for the contents..especially hay and expensive equipment).