ME_Cart Reins

Note beforehand:
it is impossible at this point (and probably never will be) to make realistic reins for animesh objects.
You cannot put particles into rigged objects, so is impossible to get anything closer to realistic looking reins than objects attached to your avatar.

This said I did my best to give us something decorative in hand while driving a horse cart.
With the ME_Horse Cart Reins you get presets
for one horse with driver sitting right, (ME_Liverpool Gig, ME_Rustic Cart)
for one horse driver sitting center (ME_Rebel carts)
for Two horses driver sitting center (Me_Blue for Two)

The reins in this pack attach to your avatar so they do not move around too much.

Manual editing of all or linked parts WILL be necessary to fit them properly to the horse /horses you have in front of your cart.
You can scale move and turn unrigged mesh objects like you can prims, to adjust the reins will be like "building on your body".
Since our horses move while we're driving carts I suggest to let the loose end of the reins end somewhere they're hidden and half way logically placed.
Make a safety copy first or keep the packed unit for that purpose in case something goes wrong.