I do a winter market garden. weeds are not an issue as they don't grow well in Ohio winters. we use simple unheated hoop houses, black landscape mulch (for heat, not weed control) and plant things that can take cold like kale, lettuce, arugula, cilantro. We also do warm weather things like tomatoes and day neutral strawberries in hoop houses usually until December

But the vast majority of what we sell in winter is stuff harvested earlier like winter squash, potatoes, garlic, onions, parsnips, carrots, rutabagas, etc..

We plant in october and harvest through the beginning of January than things usually go dormant (unless we have a warm and sunny winter than they grow through the entire season). In late Feb the crops wake up again and we harvest them. By mid March most things are beginning to bolt but it is usually warm enough to start succession planting in hoop houses.