The good smell that you experience once you get out of the car at a beach in wintertime. Would "the chilly smell of the sea" work? Or fresh / odor / some other words?
I'm not sure if this works with the smell so much but it's quite common to hear people refer to "Bracing sea air".
This emphasizes the coldness and add a bit of a harsh but refreshing or energizing feeling.
(of weather) cold and perhaps windy; (of an activity) making you feel full of energy because it is done outside when the weather is cold and perhaps windy:
We enjoyed a bracing walk on the beach.
Sea air is generally referred to smelling "briny" - which relates to the saltiness of it.
I don't know that we'd generally refer to a smell as "cold" in English. "Cold" doesn't have a smell.
Consider 'bracing' (MW)
giving strength, vigor, or freshness "a bracing breeze"
There is a whole book about sea air: sea-air and sea-bathing. It describes sea air in many ways, including briny and bracing, but my favourite is salutiferous.