This comes from personal experience of course. Two years ago, during the midst of a winter way worse then this my home had an ice dam. Here is a link to some great tips on helping prevent them, bye bye ice dam ?
Basically it is times like this, cold weather then warmer weather then more snow then some rain that are prime conditions for ice dams developing. Now although my claims experience was very good having the wall and ceiling of your kitchen opened up is not fun. Not being able to find the exact cause of where it comes in from is not fun. Crawling on a roof in the winter is definitely not fun or safe. So what can you do?