What are your thoughts on using a cover crop on my garden during the winter? 

I think it’s a fine idea.  Cover crops can help protect the soil from eroding, and it adds organic matter and nutrients back to the soil when it’s cut back and tilled in next spring.  There are many types to choose from, and I’d say winter rye is probably the most common used.  It can be planted thru mid to late October (sometimes later) and still germinate and grow.  Use 2 pounds per 1,000 sq. ft.  But do remember that you need to cut it short and till it in at least 4 weeks before you plan on planting in the spring.  You can also collect the foliage and compost it or use it later as a mulching, rather than trying to till it in the soil as well as the thick roots of the rye. Personally, I suggest adding compost, manures, finely ground leaves and grass clippings, etc and tilling them in before late fall and winter.  A light tilling in the spring and you’re ready to grow.  But whichever you chose, fall is the best time to add soil amendments, whether it be organic matter or growing a cover crop.