First thing that comes to mind is butcher paper and paper mache paste, or latex paint.
Slather a bit on the paper, start rolling it (do so at an angle to keep it going), and once long enough, let it dry.
Squeezing, adding some folds and crinkles to the paper as you go along will give great vine-like texture.
Paper mache is the cheapest option, but it won't take wet weather too well without being sealed somehow - paint or urethane or similar.
You'll also need to paint them anyway, since even the brownish-reddish butcher paper won't be completely convincing as vines.
If you do it with a dark latex paint, all you have to do after it dries is dry brush on some highlights and some leaves.
That, and the latex paint should give a level of weather resistance without having to do too much more.
Of course, if your autumns tend to be wet, it would be a good idea to coat the things in another layer or two of latex paint to really seal them from water.
If you have a Home Depot near you, they usually have "Oops" paint that's really reduced in price, and is more often than not a color that isn't good for too much other than being incorporated into a prop. Mix up some of those and see if it gives you a color that's useful for making vines.
(most of my prop paints come from Home Depot Oops paints - my favorite was a 5 gallon bucket of almost-black I picked up for $15)
Most home improvement stores have "Oops" paint that they'll sell at a reduced price - some you have to ask, some just keep it out.
When I was making my Pumpkin Lord, I wanted thick, stiff so they could be posed, weather proof vines. I took old garden hoses and a few cheap new ones. First off I used latex gloves and smeared/dabbed great stuff foam all over them. It bubbles up nice and creates a nice irregular texture on them as long as you keep it somewhat thin. Dab at the foam to get it to not just be a flat sheen and create areas of thicker texture. The foam also has the advantage of stiffening the hose. Once it dries I base coated them with brown and green spray paint. Then went back with some small tubes of art paint and dry brushed the vines with different shades of green, black and brown. Afterwards I clearcoated it to keep the art paints on and it held up wonderfully. Oh and I chopped the leaves off of some bushels of ivy. Then I used floral wire to twist around the stems and simply pushed the wires into the great stuff texture.
Here is a pic of my pumpkin Lord. If you look down along the fence you will see the individual vines strung along them. Also all of the pumpkin guys were made using the same method.
And here is a close up of what the vines can look like.
Another idea is to get some 3/4 or 1 inch wound rope (the brown type - don't know why the name is escaping me right now). It comes with several strands wound together. Unwrap then and the strands are twisted already. Add foam, paint or monster mud and paint. Will look pretty good.
Why are vines not the best material for making vines?
I have a patch of vines growing in my yard that I use. It is a mix of honeysuckle and virginia creeper. It grows plenty fast, too. I haven't cut it back in 3-4 years and when I cut it back this year, I recovered probably 1,000 linear feet of 3/4 to 1 inch thick vine in lengths of 10 to 20 feet. I didn't have any use for the thinner stuff, and that probably added up to a couple linear miles worth of vine.