Right before a strong front coming through and immediately after when the skies clear. Rain or snow - not so much. I've hunted in the snow several times and the deer just don't move, at least not around here. Wind doesn't seem to matter. Actually, the harder is blows after a front moves through if it's cold, the better. this data collection by Bent Creek Lodge, about an hour and half from me confirms what I've observed.

https://www.mossyoak.com/our-obsession/blogs/cuzs-corner/20-years-of-deer-research-on-deer-movement