In the Northwest where a lot of alfalfa seed is produced and other grass seeds it is common to bale up the plant residue from combining alfalfa seed and other grasses.
As far as mixing? I have bought a quite a bit of cover crop straw with a good amount of leafy, young alfalfa plants mixed in. Very good cow feed by the way.
Mixing straw with hay is a common way to winter cattle in some areas.