The failure mode people describe is always the same. The siren goes, the household moves, and the dog will not come out from under the bed. Minutes get spent on a dog that has never been asked to do this before, in a house where everything about the humans' behaviour has suddenly changed. A frightened dog under a bed is very difficult to extract quickly, and a small one is very good at getting somewhere you cannot reach.
The answer is to make the sequence ordinary before it is urgent. Keep a crate the dog already uses, and practise the whole chain on calm evenings: cue, into the crate, carried or led to the shelter, a treat, back out again, nothing happens. A breed rated five out of five for trainability will have this fluent inside a fortnight of short repetitions. The point is not obedience, it is that on the night the siren goes the dog is doing something familiar rather than something new.
The kit is small and it lives in the shelter permanently: a lead, a few days of food and water, a copy of the vaccination record and the MDR1 result, and a photograph of the dog with you in case you become separated. None of that is expensive. What it prevents is the two most costly outcomes of a severe-weather event for a household with an animal, which are minutes lost during the warning and a lost dog afterwards.