The local experts up here: zone 3 near Edmonton, Alberta, recommend an
expensive short clumping type of grass called "Orchard Grass" at our local
bulk seed dealer. Clumping grass doesn't choke out the trees with hard
competition and actually having grass under the trees increases the hardiness
of the trees as they die out much more easily with dirt under them when we
have one of our snow-free and -40 degree winters.