Greetings and welcome to BYH

Aside from the discussion on stanchions... as for the size of space required it would depend a lot, I think, on what breed of cow you'll be housing. I've never personally heard of folks tying their cows to a post for months at a time...

Not pro or con, just new to me (as are many things regarding animal husbandry since I'm a beginner). Can you talk to some of the folks up there who are doing what you want to do? May be they could provide some guidance/ideas? I mean, if they're already doing it... no sense re-inventing the wheel...
Most of the ranches/farms that I've ever been around/by/past that had cows, they were outside year round. This includes New England, Florida, Colorado, and eastern VA. Even in the coldest weather, the cows would just lay down out in the fields and chew cud. If it was blowing hard or wet or both, they'd seek shelter under trees, or behind a wind break, but I've rarely seen them seek or go inside the/a barn... Unless of course they were dairy and needed milking...
There were/are typically multiple pastures and the animals were/are rotated around through them. If you're concerned about them tearing up an area during the mud season, can you just limit the size of that pasture to a minimum and then once mud season is past, move them out of it to clean it up/re-seed/re-grow? Or as others have said, turn that area into your new piggery and let them till the area up for you? Since you're only talking a 1/2 dozen cows, I would think an acre dry lot for them would be more than adequate for a couple of months. It would be a dry lot scenario and of course you'll need to feed them while they're there, adding to your expense, but you'd need to feed them in a stanchion situation as well. Just build them a wind wall/lean to or run-in shelter, so they can get out of blowing weather and they should be fine.
As for the equipment housing and hay, can you purchase those quick install, carport type buildings to cover it? What will you be keeping inside the barn you'll be building, that you want to keep the hay and machinery outside it? I have to admit I'm going through the same deliberations here on barn design as I just bought my new place here and need to build a structure for many of the same reasons as you... hay, machines, animals, etc.
Hope you'll keep with us here and share some pics as you progress! I'm sure many would love to follow along with your decisions and progress! Glad you joined and look forward to reading/seeing more going forward!