If you're REALLY that worried about it, it only takes a split second to release and reset the rest.
For what it's worth, the only experience I ever had with a rest locking up due to freezing was a fall away inertia rest (spring rest). I've never had an issue with a drop-away.
If your rest is set properly, your rest should draw a bit farther back when you draw your bow, so even if it WAS slightly seized, that positive mechanical over-draw will break the freeze before the shot.
Freezing of drop-away rests is greatly exaggerated by guys that don't want to spend money on anything but a whisker biscuit. In freezing wet conditions, whisker biscuits can also 'ice up' and offer inconsistent and uneven pressure on the shaft as you draw and release the shot, so don't be led to believe that it's immune to these issues.