Wagtail
Horse servant
As Laminitis is in most cases a disease of POOR Management to me this would be a ridiculous reason for not breeding from a particular mare. There are far more important factors to consider, such as quality of conformation, action, temperament. Personally I would prefer a good doer over a poor doer any day. Not just for economic reasons but it is far easier to feed the right type of feed for the discipline if you are not having to worry about keeping weight on a horse.
ANY horse can come down with Laminitis if the right conditions exist.
Some horses are more predisposed to Laminitis and not in any particular breed.
I've had native ponies that have lived out year round and never had laminitis, I've seen TB yearlings with low grade Laminitis because of the quantity of feed being pushed into them to 'Grow them Big' for the Yearling Sales.
My Clydesdale mare is a fatty and I watch her diet really carefully, she still lives out 24/7 but her paddock has very short grass in it. Yet I have friends with Clydesdales who have to hard feed to keep weight on them.
http://www.amazon.co.uk/More-Insights-Into-Laminitis-Arabian/dp/1446156931 - Research into dealing with Laminitis in Arabians
http://www.ker.com/library/Proceedings/08/5_Laminitis_p57.pdf - Research by Kentucky Equine Research
The most recent research into laminitis has shown that at least 90% of cases are due to metabolic issues such as ems or cushings. Purely management issues account for the other 10%.