The brown rabbits can live in moderate climates like summers, springs, autumn etc. So if the temperature is getting warmer in winter, it will not affect them. The white rabbits live in colder weather like winters and snow. So, if winter temperature is increasing and winter is getting warmer, they will have problem in surviving.
So, the best answer will be option second - The brown rabbit population will thrive and reproduce, and the white rabbit population will slowly die out.