I have to empty my larger composting efforts in the fall right before and during leaf season in order to make way for the new massive influx of leaves. So, I apply late fall/early winter until I run out (saving some for potting soil). Leaves are really the limiting factor for me as they're only available for a short period. So...it's make hay while the sun shines!
Now what that means is that often the compost is not as fine as it could be...sometimes even a little chunky. I make and use so much, I'm not about to sift it. I do a little bit of that for potting soil in the spring. It will continue to break down wherever it's deposited. I tend to overfill to allow for a reduction in mass that continues to occur. However, most of the compost in fall is roughly a year old except for some finer inputs like coffee grounds, tea, SCOBY and other kombucha wastes, and pulverized/blended eggshell.