Hmm, Gandalf taking charge never seemed strange to me, although I suppose there isn't a clear "authorization" from the Gondorian leadership of the moment for him to do so. But if
not Gandalf, who is left to take charge? Denethor is not behaving rationally and Faramir ill, so there's no one in the House of Stewards that I'm aware of who could take charge. The Prince would be a candidate as another prominent leader, but he too goes to Gandalf for guidance. I suppose he could have implied permission from Aragorn, who will be the last word in Gondor once he reclaims the throne.
With regard to the weather, I thought it was interesting that the wind specifically brought the rain, given the importance of winds as messengers (the song as Boromir is sent down the river, the West wind rejecting Saruman after his death, etc). I also don't remember if rain is always
grey. Frodo's grey rain-curtain as he reaches the West was the first image that came to mind on this re-reading.