I wouldn't put any horse 24/7 on lush pasture.
It's asking for founder and other problems.
Also...just because the grass is green, doesn't mean it's actually filled with nutrients. You need to do a soil check (done by professionals, you can google someone in your area) to see just what is in the soil, which means if the grass is rich or just 'filler'
if it's not filled with real nutrients, you'll still have to suppliment. Especially in the winter time.
Either way, it's a recipe for founder to put any horse on nothing but sugar filled grass in the spring, so during that time, you'll have to be careful, too.
Ideally, you should have a dry lot.... a good size paddock where they can be in during the night. Every night. So that pulls them off grass for 8-12 hours.
You can start with 2-4 hours a day, dry lot them after that. Give them some hay anyway, just not a lot.
then increase to where they are in the grass for up to 8 hours, so a whole day, then dry lot them at night.
If you do 24/7, I think you're asking for problems (founder, thyroid issues, etc)....due to getting too fat.