Definitely separate them. I also have an arab/saddlebred (ie NSH) - not the easiest keeper ever but I absolutely love her! I have 2 mares on small property (1.3 acres) & they each stay in their own 50' square paddock most of the day. They are turned out together every day for 2 hrs in the yard, which I am constantly reseeding, etc. If I don't let them have that "grazing" time, they eat the fence boards. They get LOTS of hay though - I go through about a bale a day - the NSH gets a bit more than the pure Arab - the pure Arab can get too fat on just hay. Seems to me on small acreage it would be too hard to maintain horses without separating them. I once got a rescue case that was simply due to not separating the horses, one was getting all the feed, the other was starving to death.
Good luck - you'll love having them at home!