RRG pg 8. For any given triggering condition, forced interrupts take priority and initiate before non-forced interrupts, and forced reactions take priority and initiate before non-forced reactions.
Therefore, First Snow takes priority over "normal" reactions to the beginning of the challenges phase, like Brothel Madame. So Brothel Madam will bounce to hand before she gets a chance to trigger.
Duplicates can save from First Snow of Winter. From the RRG: A duplicate grants its controller the following triggered game ability: “Interrupt: When the overlapping unique card would leave play, discard this duplicate to save that card. (Cannot be canceled.)”