So it's better to be dead rather than living poorly (or same, or better)?
I think you assume that everyone is operating off of the same amount of knowledge and certainty that the White Walkers will destroy humanity and the only hope is Daenarys.
Folks don't know that. Hell plenty don't even believe the White Walkers will cross the wall. Even us the viewers with a much greater overall picture don't actually even know what the purpose of the White Walkers is or what they want.
Allying with Daenarys is a massive gamble. Targs are massively unpopular in Westeros and if the Starks ally with them it will almost certainly damage their chances to win the Iron Throne back in the inevitable war for Westeros that will follow the conflict with the White Walkers.