I think you might want to re-evaluate your desire for a cow considering the piece of land you may be purchasing. Cows CAN and WILL eat brush, low tree branches, weeds and such... In fact it's a good thing to have access to that kind of stuff for a well rounded diet. But they really do need a substantial grazing area. At least an acre of quality forage per cow. You said there is one acre cleared, but some of that is undoubtedly taken up by the house, driveway, garage and whatnot. Not quite enough, even if it were all perfect grazing quality. Hay can be very expensive if it is your sole means of providing food for your cow. Probably too expensive to justify having the cow, really.
The garage doesn't really sound like adequate housing for a cow... Gotta have great ventilation. And she'd need to be able to come and go from that as she pleases based on the weather. You could throw a lean-to against the side of the garage though. If a cow is well fed/watered and healthy the only thing they really need in very hot or very cold weather is a roof over their heads. A carport might work on the side of the garage away from prevailing winds.
Your land sounds great for pigs... They can glean an AMAZING amount of food on their own given a diverse habitat. Oak trees are great, pigs LOVE acorns. I wouldn't put the pigs in the garage either, as they also need ventilation. That and they are VERY STRONG and tend to lean and scratch themselves on structures... Imagine the lower walls on the metal garage bowing outward. Not so good. I'd look into getting an heirloom breed of pig that's proven to be cold hardy... Then you won't have to worry so much about housing. They don't need anything fancy. In the winter I'd gave my pigs two big round-bales of hay on the covered concrete patio of a concrete block shed we have. They tore hay off the bales to make a big fluffy nest and slept between the bales and the side of the building. Not fancy, and they did just fine. Just a note... Our cows and our pigs get along dubiously at best. We have one cow that is a total bully and hassles the pigs whenever she gets the chance.
If you reason for having a cow is for dairy, you might want to consider goats. They do very well in strictly wooded areas(they eat up, more like deer) and require far less hay than keeping a cow. They are very sweet and lovable animals to boot.
I think that if you were to spend a summer clearing trees on an acre or so of the property and seeding the cleared area with a variety of nice forages you might be prepared for a cow after a year or so.
I'd forget trying to use the garage as it for an animal shelter. With the addition of some windows or another door or two it might work for cows or goats. But pigs are really tough on shelter if they want to be... Better to make them something easily fixable/cheap than put them in the nice garage. They also make portable pig shelters you can purchase, but I don't have any experience with them. My pigs are moving to my mom's place when we leave our farm, and I was thinking of making them a small three sided strawbale structure with a salvage wood and tin roof.
A recommendation... The Encyclopedia of Country Living by Carla Emery is AWESOME. I grew up country on a farm and know a bunch about everything, and her book is still a very valuable asset to me. It has a comprehensive section on EVERYTHING. A purchase worthy of every cent of the $25 we spent.
