I've only heard of one theater cancellation so far*: Tonight's staged adaptation of the musical episode of Buffy has been postponed until January 11.
Otherwise, Imago's Biglittlethings will continue as planned; Public Playhouse's radio adaptation of It's a Wonderful Life is a go; Portland Center Stage's A Christmas Carolis still on, and as their marketing director cannily pointed out in an email yesterday, now is a great time to take advantage of their $10 rush tickets. (Their website is down but you can call get tickets here.) On the funny tip, Cheap Date is still on at Curious Comedy, and so is the 3rd Floor's Weird Sandwich. Feel free to drop shameless plugs for YOUR show that's totally still happening even if it snows.
*it was snowing when I started working on this blog post.