Its probably an easier thing to get them used to eating grass hay during the plentiful months. See if you can find a feed store that sells orchard grass, bermuda grass, timothy grass, meadow grass...any of the grass hays (not alfalfa). A bale of grass hay would last you quite a long time and is much easier than trying to pick enough weeds to dry and last for a winter.
Every so often I'll throw Dudley and the Aldabran tortoises a small flake of orchard grass hay. They mostly just mess it up, but they do eat a bit of it.
For babies or young tortoises, you can cut up some grass hay and sprinkle it over their greens and veggies, just to get them used to the taste of it. Then when winter rolls around and greens and veggies might be scarce, they will be more likely to eat the grass hay.
Weeds can be dried by hanging the upside down on a line or clips somewhere that is dry, preferrably warm and preferrably dark. Depending upon lack of humidity they will usually be dry and crumble at the touch in about 45-60 days. They can be broken up and stored in any container that is not sealed tight and in a dry location. If you use plastic bags or other air tight containers you may get mold over a period of time, even if the plants appear to be completely dry. Even under ideal storage conditions it's still always good to stir the contents up every few weeks so that moisture doesn't concentrate at the bottom or middle of the storage container. You can then crumble up a handful of weeds throughout the winter months and sprinkle on the tortoises food.
Hay is the easier way to go, timothy hay especially often has various weeds mixed in with it.
What about using a food dehydrator? I dry herbs, fruits, and make goat jerky in mine. Can't see why you couldn't dry weeds as well. Not sure what the cost would be since hydro has gone up considerably?
I find drying by just hanging can be a hit an miss, if the summer is nice and dry with low humidity it works well but if your having a wet sloppy summer you just end up with a lot of mold.
I only tried it a couple of times--- I froze some dandelion. I did it in the spring when I could find extra, just to see if it would work. I placed the leaves flat on papertowel[ it almost looked like a flower press] and did several layers. Then put it in a ziplock bag-- pressed the air out-- sealed it and layed it flat in freezer. Took some out[about 2 weeks later] and let one sheet worth defrost on the papertowel at room temp. It wasn't perfect but it was certainly ok to add with some other greens.
I usually freeze extra greens/weeds, but am trying out drying them, as well. In either case, use by chopping the greens/weeds finely and mix 'em in w/ Spring Mix and/or soaked Mazuri Tortoise Chow at feeding time.
Freezing greens/weeds does changes the texture somewhat and some think freezing robs very slightly them of nutrition (but some say drying greens/weeds does, too), but my torts find thawed green/weeds to be perfectly acceptable and you can augment w/ powdered vitamins/calcium quite easily.
veggies are available in our local grocery stores year round.. prices vary.. and it depends on what type of tort you are feeding and how much you will need.. but the getting them used to grass hay and buy a bale at a feed store is the cheapest way to go. If you cant store a big bale.. then you can get the bagged variety at walmart. Its nice a clean and stores eaisly.