Most Spring Turkey Seasons are designed to start after the the peak of the mating, to preserve the species.

The weather has very little to do with the timing of the mating, whereas; it is determined by the amount of daylight. If it is cold, cloudy or raining throughout Spring the turkey will still mate...

If your toms are henned up, then typically it is still very early in the mating season. If anything that would mean that your season opens too soon.