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The short answer to your question about best time for adding compost to your vegetable garden is...it depends!  It depends on the quality of your compost and its maturity (is it finished?)  Rather than go into all the what ifs, here are two links that will help you make an informed decision.
Thanks again for your question!
http://www.gardening.cornell.edu/factsheets/orgmatter/#when
http://www.ext.colostate.edu/mg/gardennotes/243.html

Thank you for answering my question. I read both materials and could not find my main cause of concern if adding the compost in the fall. What will be the quantity of nutrients lost from about beginning of November and the time to transplant seedlings in the garden that is last third of May here in Cleveland OH area? In a typical winter here there will be several cycles of snowing and melting and the water will leach nutrients deep in the ground beyond the 8in that the vegetables in my garden develop roots. Actually I made measurements and a lot of them don't go more than 6in deep, some (like melons) even less. The question is what is the percentage of lost nutrients? Would you be so kind to point to some studies treating this subject? Thank you again. Mihai Gata

Hello,
I will add good, finished compost to my garden either in Fall or Spring, but I prefer Fall.  I have more time available and weather is more cooperative.  Spring rain or long-frozen soil means you may only have a few days to get the garden prepped.  If the compost is already on it then you can skip move right into other work.  Fall applications are already settled in and populated by the critters that use it.  Planting in newly applied compost (especially less-than-mature-compost) can be difficult and :mucky".  If you spring-apply I would suggest giving the compost a week to settle into the soil before planting; more if the compost is young.

As for nutrient loss, remember that compost is essentially nutrients locked into organic compounds.  It takes biological degradation to free up those nutrients and that release will slow down when the critters slow down in winter.  Yes, you will lose available nutrients (primarily nitrogen, others are more long-term) but more will be released when soil warms in Spring--just about the same time you begin to garden, what a coincidence!  Can you quantify that?  No.  Water soluble (N) will be lost at a greater rate.  Without an analysis of compost content (which will vary greatly), temperature to gauge the rate or new nutrient release, and irrigation for leaching you would be hard-pressed to actually quantify the nutrient flow.

Along the N Coast, I would go out on a limb and suggest that any available N would be lost through winter, but be replenished when the soil warmed up next spring.  But, you would benefit from the long term presence of the compost during the non-frozen weeks.

Spring application would not see that N loss.  Timing and workability are my only cautions against spring application.  I do apply in the Spring as well but concentrate my efforts on fall application along with a cover crop.  These past two years, that strategy has paid off when the garden remained unworkable through March.

Tim
North Ridgeville, OH

Thank you very much. Your response really clarified me about this subject. I thought also about cover crops. The problem is that the vegetables and the flowers in the garden die usually after the first snow when is too late to sow. You think I should take of the weed barrier and seed a cover crop between the rows and try to step as few as possible over it. What cover crop would be better for a 50x50ft garden? Right at this time I harvest at every 2-3 days tomatoes, eggplants, peppers, broccoli, cauliflower, beans. All the apiaceae have green leaves and I harvest the roots & leaves by need. The dahlias, gladioli, nicotianas and petunias are full of flowers. Even the calla-lilies are still flowering here-there. If I sow all the space in-between with a cover crop will it not be too crowded? Thank you again. Mihai Gata

I think I need to ask where you are geographically before I respond.  The tag on your original note indicated Lake County OH, but over here everything has been well frosted and not much looks as good as you are indicating in your garden.

Thank you very much again for your time. I live in Mentor (306 area, North of route 2). I made this morning a few photos and I attach 3 of them at a reduced resolution. In the 2nd part of October there have been a min air temperature of 31F, one of 35F and two of 39F. The soil min temps at 4-5 in deep have been over 50F except the day air was 31F when there has been 48F. The max temps have been around 60F (I have the whole table if you are interested). Only the cucurbitaceae and okras (in the back) didn't take well the thermal regimen. The next few days the max temps will be in the 70sF and sunny so I shall try to take some details with my camera. I can provide them if you want to have a look. Thank you again. I enjoy learning from you. Mihai Gata

I don't know why didn't post the photos. I try again and if it doesn't work this time too I can send them at an email that you can provide me with at h/g/s/-/a/l/l/\\e/a/r/t/h/l/i/n/k/./n/e/t ... take all slashes (/) and replace the double back slash (\\) with "at" (protection against email harvesting robots). Thank you.

Thanks for the additional info.
Given the current conditions I would suggest you could still get away with a winter rye cover crop.  By the calendar it would seem too late, but winter rye planted now will sit on the soil and develop very slowly throughout winter.  With a mild Fall, you will still get decent development.
Winter rye must be killed and worked in a few weeks prior to planting as it has germination inhibitors that keep other seeds from germinating.   It can also be a weed problem if not totally killed and worked in.
Mustard is also a good fall cover crop and some have weed-inhibiting characteristics as well.  However, it will not do well this late in the season.

1) I looked with another browser an I saw the images were there but they were not displayed! 2) If I understand well I can just spread the grains on the ground. It is not necessary to work them in. As you may see from the photos most of the ground in my garden is covered with weed barrier so I have to take it off. The problem is that I still have to walk between the rows. Wouldn't this damage the rye? 3) I was normally leaving the weed barrier during the winter, roll it on to till and then roll it off right back. When is the best time to seed rye considering the condition at #2? How much time takes to germinate? 4) Do you want to see close-ups of vegetables. I have now. Thank you again.

The rye would probably not thrive where you walk frequently.
I do not need any other photos.
If you want to add organic matter via cover crop, then rolling up the weed barrier is the only way to go.  I would sow as soon as possible.

I think now I have more knowledge than I asked for initially and we may close this discussion here. This is very helpful information. I thank you very much for all your help. Mihai Gata