I recommend that if you do bring her home split the pasture into two sides and put her in one side while the other one grows and then switch so that the other pasture can grow. Also make sure she has a companion animal that she gets along with ha ha ha
Check with whatever state you are in! The states have laws for that. In VA I know you have to have a minimum of 1 acre per horse with at least a 3 sided shelter. If you don't check first there is a chance that someone could turn you in and then they would take her from you if you didnt provide appropriate housing. Im not saying 1/2 acres isnt enough I would just rather see you on the safe side than to move her and get into trouble.
I have one horse on 1 1/2 acres and that is really hard to manage. We are in a drought and there is nothing for him to eat. Hate to think what it will be like in winter. I would be inclined to say no 1/2 an acre isn't enough even with stable. The horse needs to have enough room to go for a good run. Also the paddock won't have a chance to be rested at all. You will prob get loads of weeds and pasture quality would go way down.
Ya and I know im planning on trying to put a round bale out there when she's turned out to try and save the grass lol and when she's in the stall ill cover it up just in case if it rains. And yes she will have a companion either my dog [lexi likes dogs] or get a goat.
I don't think a dog will be a good companion as dogs are predators, whether you want to think of your dog as one or not. I'd suggest getting the goat. Also check your state laws as mentioned and make sure you aren't required to have 1 acre per horse. Sure you can have them but what are the space limitation laws. Make sure you check that or as mentioned, they'll take her away for improper housing.