IMO, there is no such thing as extra hay, I don't believe hay or grass should be rationed. Mine have all they want 24/7. Unless he is working.
I have two horses with metabolic issues - they get rationed on both grass and hay. The hay is right down to the pound on the hanging barn scale
That being said, I "slightly modify" their rationing on freezing cold nights and on nights when the big storms are coming thru - like last night - tornadoes -- who wulda thunk we'd have tornadoes in January, but they were out there.
But I also get my hay tested, so I know how far I can push the "extra" button where the metabolic horses are concerned
I don't feed rounds for many reasons but to reiterate, I have two metabolic horses who don't need to be eating until their hooves are pointing skyward.
Last week is the first I have thrown hay in the morning that everyone stops and takes a few bites before heading to pasture. We also have had good pasture up until now.
Even at that, my four are only going thru about 20 lbs of flakes daily - there's still enough grass that they're happier in the pasture.