Depending on your local temperature, you can start by re-caulking the exterior bottom plate of the door. Run a generous bead along the length of the plate (and higher along the sides is necessary) and do not let it get wet or freeze until it cures. If you are already snow-bound, you might have to temporarily tent the area for a few days so it is warm enough to cure the caulk. I would do my best to keep snow from piling against the exterior door.
Anything more destructive would probably solve the problem for years ... but I doubt you want to take that route just yet.
GOOD LUCK! Let us know what happened ...