Need Help... With vines

Ok I have a 60 acre horse farn with wonderful no clumb horse fence on pipe. It is actually a pretty fence however I would really like to cover the area that is considered my back yard with a pretty vine. I have been working on the farm for almost three years now and I am finally at the fun stuff point however I can't find any fun in it right now.
First I am looking for a no poisionus plant for dogs, cats and horses any any other animals that might decide to come live on my farm (which is every living being in a 100 mile radius I think). I finally found Cissus rhombifolia and thought perfect! Safe for everyone and something that will look great all year round but now I can't seem to find any information as to if it will grow in Texas. I am in North Texas close to OK (about an hour from Dallas). I water daily as I have sod that I spent fortune on, 6000 square feet and shrubs. Any idea or suggestions for something that will stay green or some color year round safe for animals that grows very fast? I know I am asking for a lot.
Second I am looking for a bush type plant that my grandmother grew when I was a child. She is now gone and I can't ask her the name. She called it "A minature thornless running rose bush" although I highly doubt that is the actual name. I am not sure if it is even a rose bush. Any idea what this plant might be called?
I really appreciate any help or suggestions.

Hi Sarah,
I don't know anything about the vine you mention above but I can tell you I have red honeysuckle growing on a trellis in my yard. It's evergreen and very pretty. Deer will eat it so it's not poisonous and the humming birds love it. It's doesn't take over your whole yard like the yellow (Japanese) variety will either. We dug ours up from out in the woods so it's a native variety. We were lucky to find it because the Japanese honeysuckle spreads so fast that it's killing out the native red honeysuckle.
I also don't know anything about your grandmother's rose. Too bad--it sounds pretty. I have 99 percent native flowers in my yard because they feed the birds and insects. Too many flowers have been hybridized and don't offer anything for the wild critters.

I wonder if your grandmother's rose was a Lady Banks? It comes in white or yellow, they are thornless, and the roses are small. I have a yellow one and it's a prolific bloomer. You might run a search and see if you can find a picture--you might recognize it.

Dear Sarah,
Well, my goodness, your region of Texas seems so far away from me right now. but if you have vines in mind...have you looked into Uva Americana? This is the strawberry-tasting grapevine which is indigidinous to America...it doesn't need cutting, grows sweet and wild, but delivers a bounty of grapes in the fall. I am currently gardening in the wilds of northern Italia, and in spite of the hot summer and cold winter , my Uva Americana do well. They were gifted to me by someone who knew that I'd missed my native land. But the ladies here in my valley....oh, my. They are wild about the grapes from America. Even with the normal Vinticulture in north Italia. Nothing spreads faster than success. Look into it, if your growing zone and your temperement allow it.
B.-

Circe33, Do you know where I can get one of these vines? I've looked everywhere, is there another name for it. I saw a couple of places where you can buy the grapes but I want the plant to grow my own grapes and have no plans right now for making wine right now so I do not need a 'Kit'. :)

Another grape vine to consider is muscadine. They are a southern native and quite tasty.

Are they easy to grow?

Muscadine grapes are very easy to grow. They're very hardy too.

Sounds like a good plan, Thanks a bunch! :)