Horses can live among trees, sure. If you clear the fields and sow seed, you would need to keep the horses off it completely until the grass is well established. Some people might allow some limited grazing around month 4 (depending on YOUR location/weather/growing season/type of seed sown,) but you could require up to 12 months before it's strong enough to handle regular grazing.
That said, 2.5 acres is not much land. Once you subtract a home, driveway, barn/hay storage, you'll have less than 2 acres left for animals. If you want to keep grass in that space, you'll need to carefully limit grazing and foot traffic so it gets time to rest and recover. You'll need to be vigilant about using a sacrifice paddock when the ground is wet, otherwise they'll churn it into mud in a jiffy.
When I started my house hunt, I though 2 acres was perfect. I ended up with 6.25 acres (4.5 acres of dedicated pasture) and couldn't imagine having any less for my two horses! We had TONS of rain in 2018 so my horses spent a LOT of time eating hay in the sacrifice paddock...
~Reserved Cash, 2011 AQHA gelding~
~Lark, 20-something Arabian mare~