Yes, they will continue to ripen. Harvest when brown and dry. However, note that many varieties will not breed true from seed and generally speaking, there is a low germination rate for hosta seed even with stratification. Thus dividing the plant will generally give you better results and is healthier for the parent plant in the long run.

If you are looking for specific varieties be sure to check out the Hosta Forum here.

Dave

What kind of hosta do you have that does not disappear in the winter in zone 5??? THat must be some seed worth saving!