I think most people, if you asked them to describe how weather affects a cell tower, would describe them as working in basically the same way that Iridium handsets do: "clouds in the sky, signal goes bye." I.e., the signal would be "choppy" on the interval of milliseconds, with packet retransmissions covering it up up to some tolerance level, but failing entirely and instantaneously if the weather was bad enough.

I imagine they would think this, even though they know intuitively that cell signals are more robust than that in practice. They don't know why they know that, and they've also been taught something that conflicts with that knowledge, so depending on which order their jumble of thoughts comes to mind, it might go either way.

(Also, something I'm curious about, as a tangent: now that atomic clocks are getting cheaper, are cell towers using them to add fault-tolerance to their precise timekeeping requirements, in the way that e.g. undersea-cable head-end switches do?)