I put pieces of cardboard on the dirt floor of my unheated greenhouse. Periodically, after they become soggy, soiled and mangled, they go into the compost bin.
Last fall I tried a compost pile in the greenhouse and the results were disappointing. I created an enormous mess in there along with lots of flies. I'm tempted to try it again this spring but hopefully the snow will continue to fall here until that temptation passes.
For gardeners, this has been one of the most discouraging winters we've had in a very long time. We had two large snowstorms earlier this week and today's coastal storm was supposed to stay south and just clip us with a dusting. I just came in from shoveling 6 inches of very heavy dusting with no end in sight. Gosh, we need a break.
"Good gardeners do not have green thumbs. They have brown knees, soiled hands and big hearts."