There are varying opinions on this issue. I too hunt just about every chance I get, regardless of weather. As such, I tend to track patterns. I have noticed that before a storm, usually 2-4 hours before is pretty good for coyotes. But that can just be a local occurrence, and I accept that.
I will also head out right after a long storm front, one that might have pinned them down where they are going to be hungry and more than a little stir crazy.
Weather definitely effects them, of that there is no doubt. But to what extent I think is the real variable. Around here we notice that if there is a cold snap, coyotes tend to lay up. But if the cold sticks around, they will pretty much come into any sound you throw out. So if the temps are bouncing up and down a lot we see their interest drop.
I also look for trends in the baro pressure. Seems like if it's falling their activity drops around here. But if the pressure is high or rising they are moving around.
We also use the 3 strikes rule. Call the same exact way 3 times in a row. If nothing shows, change something. Volume, calls, stand time. Then try 3 more stands. Keep doing that and when they show up, look at what your stand is like and start applying that to your patterns.
So track the trends and put that information to good use.