There's a lot of debate whether blankets help or not, but here's my two cents.
My show horse is blanketed, and usually he doesn't start really shedding until the end of April, but he's shedding now. :) I know that horses blanketed during the winter have smaller winter coats (It also makes it lay flat so it looks thinner, too). And I know that when horses sweat, it helps encourage their body to go, 'hey, the light ain't right but it's getting hot! SHED THE COAT!' so if it's hot and my horse is drinking, I leave his blanket on to encourage it. (I'm not taking about his entire body sweated up, lol! Just a tiny bit under the blanket.)
Good luck! I'm in the same boat as you lol