Do you think cows would like a nice leafy green salad as a treat once in a while during the winter instead of hay all the time?

Cows will eat plenty of different kinds of herbs, vegetables and weeds given the chance.
If you're talking leafy green salads, I think they'd love kale, English spinach, pak choy, parsley, sorrel, broccoli, beans, peas, watercress and many others.
If they're dairy cows, greens are essential to keep up milk production through winter when closed up in barns.
Alfalfa hay is the usual means - though there are also pellet feeds and supplements. The latter can cause problems due to cheap or illegal ingredients or poor manufacturing processes (moulds, ergots, yeasts = bloating or illness).

Having four stomachs and the capacity to pulverise their cud, their can survive efficiently on roughage with poor nutrients, but milk flow will stop without high nutrition and energy. 
The type of hay matters. Just oaten or wheaten hay would quickly produce a calcium deficiency. So can some kinds of grass hay, especially if not cured properly or if it's more than two years old.
For non-lactating cattle,  an equal amount by weight (not volume) of alfalfa hay should be provided to ensure the right balance of calcium and phosphorus. Lactating cows should get 10-20% more alfalfa. Pregnant and lactating cows should get 50% more, as should calves and youngsters up to 2 years old.
Insufficient calcium leads to loss of bone density. Cows can then die or must be put down due to the pelvis breaking during calving. Calves with insufficient calcium can develop rickets or easily break bones.
Same applies to horses and other herbivores kept indoors through winter. This post was edited by inky at December 28, 2020 9:04 PM MST