Miniature cymbidiums should grow and flower quite nicely in Arkansas. I am able to flower a few here in Central Florida. The secret to flowering, I think, is to expose the plant to night time temperatures of fifties in the fall. Sept. is probably the key month for setting buds so if you can give them fifties in Sept. the rest is gravy.
I am in North Central Arkansas and I have no problem growing Cymbidiums here. I have cut back on them because they take up lots of space in the greenhouse.
The nights are lots cooler here than the days and I leave my Cyms outside for all but just a few months of the year or when freezing temps are expected.
They are tough plants and given proper care will bloom beautifully here.
Congrats on the land and good luck with your cymbidiums!!
You should be able to grow many more cymbidiums in Arkansas than you were able to grow in Florida due to the larger seasonal temperature variation. Just be careful with some of the warmth tolerants you bring with you from Florida during the colder winters in Arkansas, especially the ones with Cym. ensifolium in it.