I am not a breeder but I will share my experience with my one mare and foal.
I separated them where they could see and not touch and waited and waited and waited.....the mare never really looked dried up. Her udder got less hard, but she still had these huge, full teets. For some reason I thought they would get all flabby and they never did.
Finally I put them back together (it's been 3 years now so I don't remember how long I kept them apart) and she would no longer let him nurse (would try to kick him actually), so I kept them together after that.
So the "baby" is now a 3 year old, never nurses, but momma still has enlarged, full looking teets and will occasionally secrete a little drop of milk on the ends of her teets from time to time. I'm sure if I milked her I would still get milk. My mare has been a career broodmare before I got her though, so I guess that's just what her body has become accustomed to. Her teets are definitely enlarged from all the foals she's had.
I guess what I'm trying to say is, I kept waiting for her to "dry up" and it never really happened. I would think if you mare hasn't had very many foals she would actually dry up, but if she has had a bunch of foals she may always have a milk bar.
I think my mare is the exception to the rule though. I have never seen a mare with a droopy udder like hers. She has had 10 foals that I am aware of.
(She has a new career as a trail horse now and really enjoys it).