Like game fish, deer have a pronounced comfort zone or, rather, a preferred temperature activity range which influences daily movement patterns. Temperature becomes even more critical to whitetail movement as the rut approaches and then again late in the season in colder climates. I.E. Unseasonably warm weather during the rut will slow down deer movement until the cooler evening hours while inordinately cold temperatures will cause deer to feed earlier in the day late in the season.
Precipitation, whether in the form of rain, snow or anything in between, often influences deer movement intensity. Periods of heavy rain and/or snow, for example, may cause deer to bed down for long periods of time between feeding activity.
Although sky conditions in and of themselves may not influence deer activity, they can certainly portend of upcoming weather events which can definitely cause deer to get on the move or lay low.
Wind speed and direction play a critical role with regard to whitetail behavior. I.E. Whitetail deer movement is often greatly reduced at anything over 15 m.p.h.