Oh sure, weather has a bearing on gobbling activity certainly and turkey behavior overall. There are now some relatively comprehensive studies done by a couple of southern universities that have hi-tech microphones out and compare the recorded gobbles v. wind/temp/barometric pressure, maybe some other parameters too.
No doubt cold and wet shuts the gobbling down. Wind also. I think turkeys hate wind. Every thing in the woods is moving....and to a turkey, any moving thing could be a threat. It also robs them of their hearing. Fog denies them of their vision and a fog bank rolling into a ridge or mountain side will shut them down as well.
Another factor I believe in is light. The lengthening days and increased light after short winter days supposedly trigger something in a turkeys noggin to signal him to start his breeding cycle (there are likely correct biological terms for that, but they escape me just now). What I have noticed is that the brighter and nicer the morning, the more gobbling activity I am likely to hear.....as a general rule. On overcast "flat light" mornings, gobbling seems to diminish...again broadly speaking. Hunt turkeys much and you will hear exceptions to all of those statements, but as a guide, nice days are better than days with any sort of inclement weather.
In a perfect year, gobbling will peak just before the season comes in, the logic being that a goodly amount of breeding has occurred before we start killing 'toms and disrupting breeding activity. Things will taper off then a second "late peak" will occur towards the seasons end, this occurring as hens begin to sit their nest and gobblers find themselves alone without willing companions.
I think weather swings effected N. Alabama's spring season this year. Wild temp swings leading up to the opener, tornado activity and high wind days combined to reduce gobbling (at least in my observations). I never heard a bird 'til March 21st, heard birds first two days, then went 12 days before a gobble (..."a"... gobble mind you, not even a number) and went 15 days after that 'til I heard a bird on 1 & 2 May. On top of that, I think the gobble of 15April and 1/2May are the same dang bird!