In my research and collecting of eye-wear (glasses), there were around the ear wire rim glasses for those who rode horses.
In a photograph of General Grant's daughter, she was dressed up (as a child in costume) as the old woman in the shoe. She (Grant's young daughter approximately 5-7 years old), was wearing rimless eyeglasses similar to the pair I found in a 1812 writing slope that was wedged in a secret drawer.
A Ophthalmologist who collects eye wear where I am, and a Civil War buff -- has identified several characteristics for 1860.
They have no eye pads; they have supporting sides to the glasses that can be -- wrapped wire that can be bent, to include to wrap around the ears when necessary; that slide mid ear-piece that are adjustable to the wearer; weave wire ear piece with a 'tear' drop or 'paddle' end and those that slightly bow but has pressure to keep them on the head at the back of the frame by tension. Lenses can be round, oval, hex-angled, clear or tinted. Rims and side ear supporting pieces can be as thin as the interior of USB wire. Some are slightly wider. I agree with Johan_Steele's description of screw and lead inserted pins where they fold nearest the frame and or lenses.
Having to wear glasses -- the equestrian glasses would make perfect sense, as I do have the other straight ear supports. They wouldn't stay on if I were to take a few fences in a hunt, or jerk my head around if I was in a Cavalry duel.
A few of the eyeglasses I have came with eye-glass cases. They lay very flat and in a case that is as long as the folded pair of glasses, approximately 7 inches long, about a inch and one-half wide. When they are pulled out the pop up a bit with the spring in the metal --silver metal and brass. Rarely are there gold frames.
Some frames are 'stamped' with the brand/maker. Because my 'main source' is a collector they have books to catalog known eye-wear shops and eye-doctors.
The problem is 'availability' and 'serviceability' of these eye-glasses. Sometimes wearing contacts is the solution or, have one pair for non-combat and another less authentic pair for out in the re-enactment field.
I would suggest that more canvasing be done among the re-enactment community and or Ophthalmologist historian. Smithsonian may be of assistance as perhaps the Museum of the Confederacy, as I believe they might have General Lee's eye-wear in the collection.
President Lincoln is to have had eye-glasses and may be on display at Ford's Theater Museum, in Washington.
http://www.americanheritage1.com/presidents/abraham-lincoln.htm
http://memory.loc.gov/cgi-bin/query/D?scsmbib:1:./temp/~ammem_4C0b::
The items consist of one pair of gold-rimmed spectacles with sliging temples and with one of the bows mended with string; one pair of folding spectacles in a silver case;[excerpt] 7.) Glass lense cleaner and buffer 8.) Glasses case 9.) Lincoln's eyeglasses with name on inner stem. [end of excerpt]
http://www.flickr.com/photos/library_of_congress/3253743680/
and...
NOTE: These two sites have famous people's eyeglasses, e.g. Lincoln, Lee, Jeff. Davis, etc.
http://www.antiquespectacles.com/treasures/mistaken.htm
http://www.antiquespectacles.com/people/people_present2.htm
This may be of help for your modern purchase for eye-wear for re-enactments.
http://www.blockaderunner.com/Catalog/catpg28b.html
http://www.focusers.com/mcallister.html
and originals they did have for sale:
http://www.blockaderunner.com/other/eyeglasses.html
http://www.eyeglasseswarehouse.com/pages/civilwar.html
M. E. Wolf