Every lawn guru on every forum for the past 10 years or so has strongly recommended mulch mowing every time. The only time you would collect the clippings would be if you were getting ready to overseed the lawn in the fall.

I don't even know where my lawn mower bag is. I don't know where the bag is on the mower I replaced. I have not collected clippings in 40 years of mowing.

Clippings are used as food for the soil microbes. Inasmuch as those microbes generate heat, then yes, the clippings can protect from cold, but I would not rely on this to keep your grass alive below 30 degrees. Most grass normally goes dormant in the winter anyway.