Brood breaks, mainly just interrupt the exponential reproductive increase of the varroa, which helps, at least somewhat.
But I agree with VTBeeeGuy, a break without treatment, is not particularly effective as control strategy. Warm season, beekeeper-induced brood breaks, in the absence of treatment seem to me to be more costly to the colony's long-term success than anything.
The natural brood pause of early winter (when coupled with the reduced flying opportunities which cause the hive or yard to be isolated from re-infestation) is the most effective treatment window of the whole year.
But in answer to the OP's question: yes, the wretched varroa will survive the winter brood pause. And even in frigid, snowy Livingston County NY (I live in Rensselaer County, which isn't much balmier) your queen will be laying again in a few weeks time. So, the varroa will be back in the breeding business by the end of Jan. Unless you seize this rapidly-closing window to treat them with OAV. In which case. nearly all the varroa (90+% of them) will be killed in a single treatment. And because no bees will be flying in or out of your yard for a couple of months, your bees will have the first couple of months of their spring build-up nearly mite free.
Nancy