During the spring pasture quality tends to be different than in the late growing season or during winter. Younger grass tends to be richer and more nutritious than later in the season.
People often feel it's important to slowly introduce their horses to spring pasture. Pulling a horse off spring pasture after an hour can be difficult---horses are reluctant to come in surrounded by green grass. However, although many feel that that gradually introducing their horses to spring pasture is important for digestive health. Spring pasture has a mix of both green and dormant plants. If you pull them off this and put them back on when everything is green they will just gorge themselves. If you keep them on the pasture and they start to search out the little green stuff, they will be acclimated to the changes. However, if you do have insulin resistant horses, gradual introduction might make sense. New pasture growth high in fructans might cause some problems for them.
There is some risk of colic and founder when turning horses onto fully green pasture cold turkey but the odds are most horses will be okay. But if your horse is completely new to pasture turning out for an hour each day and extending each day by an hour or so to gradually change them over is probably what most veterinarians would recommend. One solution is to put a grazing muzzle on your horse if you're concerned. That way he won't overeat and you don't have to chase him around the pasture trying to convince him to give up the smorgasbord.
People who have good pastures can count themselves lucky because the nutrition is very high in living forage. So do you need to supplement with hay? You can but you will probably notice that your hoses will ignore the hay altogether.
Note: For information on what pasture plants grows best in your area consult your local USDA extension agent.