Soil "almost frozen"? Really? You are a thousand miles south of us, and we spaded up and raked smooth the soil in a vegetable garden yesterday. I suggest glyphosate, wait a couple weeks and till-in whatever remains. Quackgrass will be the most troublesome. Keep in mind glyphosate will not persist and it will not kill weed seeds. Keep in mind that on such sites, weed seeds will sprout vigorously next year...particularly when the soil temps hit about 80. Good chance that quackgrass roots and similar rhizomes will also be a problem.
A pre-emergent like "Preen" applied in spring might help slightly...of course, it will prevent most seeds from germinating--so--your gardener would have to use plants, not seeds, in treated areas.
Ric makes a good point, plastic film will stop weeds, but a huge crop of weeds may grow up under the clear type--as the weeds benefit from the warmer temps in spring.