The only winter grass that I've seen planted in our area is annual ryegrass. Thickness/density of the grass cover will be dependent on how much seed you put down. It will help to minimize erosion, and you might want to consider mixing some centipede or other grass seeds with it to help hold the soil after the rye dies out. You will have to control the height by mowing; sorry, I don't know of an annual that is low-growing and low maintenance.

If you want to minimize mowing needs overseed with perennial rye instead of annual. It's more expensive, but it's slower growing and holds up better in heavy rains.

And thanks for the reminder! I need to pick up some next week for the front yard.

...and they say the perennial rye won't survive the heat, so you don't have to worry about getting rid of it later. I've heard several experts recommend it.