Tom Wahl of Red Fern says in this video
https://www.youtube.com/watch?v=PAf1lUrqSq4 that typical pasture mixes of grasses and such compete with his chinese chestnuts too much, so he finds that planting lower-vigor grasses and such that compete through persistence, not vigor, works better, and saves mowing, as they need less mowing to leave a clean, low surface that his PYO pickers can harvest chestnuts off of.
I've been searching out acid-soil-tolerant nitrogen-fixing low- and slow-growing groundcovers to complement chestnuts.
Prospects include:
Ceanothus prostratus Mahala Mat - seed is doubly-dormant from plant; needs both cold- and heat-treatment, reportedly. Reportedly found in high and thus winter-cold, well-watered areas of the coast range of the West coast.
Lupinus brewerii Brewer's Lupin: A low-growing lupin adapted to acid soils.
Lupinus bicolor Miniature Lupin: I have these growing in chestnut seedling's pots, for future grandcover use.
Trifolium brewerii Forest Clover: low-growing and shade tolerant, I believe.
Trifolium repens White Clover cv. 'Microclover': Low-growing, acid-soil tolerance uncertain.
Lotus corniculatus Birdsfoot Trefoil cv. 'Plena'/Pleniflorus'/'Empire' These are prostrate or nearly so.
Medicago lupulina Black Medic cv. 'George' I have not yet found a seed source for this University of Montana-bred release.
What has worked for you?
