It is unusual for a strong hive to starve and die within inches of a cluster, although it can and does happen. A weak hive will a lot quicker though.
Yes, that January/Feb thaw can hurt the bees, although it is much worse if it happens in March (here in zone 6). You are best off making sure they have enough honey and that they are adequately protected, and then just stop worrying about them, there isn't much you can do.
On another note...my observation hive has a tiny cluster and 1.5 frames of honey, yet the bees have always made it to spring. It is 70-80F in that room all winter, and they don't start raising brood till March. (Then they crash in May when the beetles, who enjoy the 80F room, massacre them)