Winter annual cover crops, winter rye (Secale cereale L.) and hairy vetch (Vicia villosa Roth), can reduce weed density and build soil quality in organic production systems. There is interest in integrating cover crops and reduced tillage with organic vegetable production, but few studies have been conducted in regions with short growing seasons and cool soils such as the upper Midwest. We evaluated no-tillage production of tomato (Solanum lycopersicum L.), zucchini (Cucurbita pepo L.), and bell pepper (Capsicum annuum L.) planted into winter rye, hairy vetch, and a winter rye/hairy vetch (WR/HV) mixture that were mechanically suppressed with a roller–crimper at two locations in Minnesota. Average marketable yields of tomato, zucchini, and bell pepper in the rolled cover crops were reduced 89%, 77%, and 92% in 2008 and 65%, 41%, and 79% in 2009, respectively, compared with a no-cover control. Winter rye and the WR/HV mixture reduced average annual weed density at St. Paul by 96% for 8 to 10 weeks after rolling (WAR) and hairy vetch mulch reduced weeds 80% for 2 to 8 WAR, whereas at Lamberton, there was no consistent effect of cover treatments on weed populations. Winter rye and the WR/HV mixture had higher average residue biomass (5.3 and 5.7 Mg·ha−1, respectively) than hairy vetch (3.0 Mg·ha−1) throughout the season. Soil growing degree-days (SGDD) were lower in cover crop treatments compared with the no-cover control, which could have delayed early vegetable growth and contributed to reduced yields. All cover crop mulches were associated with low levels of soil nitrogen (N) (less than 10 mg·kg−1 N) in the upper 15 cm. Rolled winter annual cover crops show promise for controlling annual weeds in organic no-tillage systems, but additional research is needed on methods to increase vegetable crop yields in rolled cover crops.