I have a lot of leaves on my lawn (in Oklahoma). Will it hurt the grass if I leave the leaves there over the winter?
Yes, if they get matted down - just like covering the grass with anything else would - by reducing sunlight and air circulation.
Less importantly, leaves will compete with the grass for nitrogen - they consume it in decaying.
Oak leaves are especially bad because they're acidic.
Some folks have good results with shredding leaves and leaving them on. Not me. I suspect this may work well (or at least better) if you fertilize a lot, which I don't.
Grass still grows in the winter, except when it's very cold - just a lot slower.
If you mow over the leaves with a lawn mower and chop them up, they will go between the blades of grass and decompose into the soil. The grass clippings and leaves chopped up make a good carbon/nitrogen ratio for composting. If your leaves are a quickly decomposing type like cherry, a thin layer will not damage the grass during winter, but oak leaves will mat down and deprive the grass of light and oxygen.