I can't answer the part about whether or not the seed pods should be left on -- I always let seeds ripen on the plant. However, there's a very useful online seed germination guide that says the seeds need up to 3 months at 68 degrees F (20 degrees celsius) to germinate.

Here is a link that may be useful: Ontario Rock Garden Society Seed Germination Guide

Hi Leslie, Just let them ripen on the stalk. Yes, you can winter-sow. I tried this last year, and it works great. Just drop the seeds on moist surface. You get mostly (like 99% by my inexpert estimate) all green seedlings. I did get one little golden guy - I picked him out with a toothpick and potted him up. It's not a fast way to get new hosta, but it's kind of a fun experiment.