Please see the study results reported from the poster attached. It seems that the results also to do with the morphology of a plant species. They conducted photosynthesis study under sunny day and cloudy day, and tried to compare the results.

They found:

"In this study, we compared photosynthesis of Engelmann spruce (Picea engelmannii) shoots during cloudy and sunny conditions at the alpine-treeline ecotone, near Centennial WY.  We demonstrate for the first time that conifers exhibit similar photosynthetic rates under sunny and cloudy conditions, supporting the hypothesis that conifer shoot morphology may be an adaptation to maximize photosynthesis in environments typified by diffuse light (of cloudy day)."

I don't know what you are looking for, but in your question, two factors are playing a role: light (cloudy sky) and temperature (winter, that besides also changes light intensity and Spectrum, compared to summer conditions), so the answer may be equivocal.

Dear Dr. I think that photosynthesis do not dependent just to light

and other factors such as achieved water, temperature, genotypes, types of plant, stage plant, season and ... are very important.

Best Wishes

I think it depends on the species and the light level on those cloudy days and whether you are using your won light source, such as present in the LiCOr 6400. Previous experience (or literature) with the same species can aid for the decision making). If using the artificial light source, sunny and cloudy times for a given day should not matter much as along as it not very cloudy for extended period of time (like over an our or so). also, Many row crops photosynthesis saturates around 1500 micro mol. if the think clouds filtering near this light range, the measurements can be done using the artificial light source as in the LiCOr.