Draughty double-glazed door / not sealing correctly

I have a couple of external doors that have suddenly become noticeably  very draughty with the high winds we are having at the moment, the draft is coming through at the bottom - mostly on the hinges side. I assume it's something to do with a dropped hinge (?).

Is this something a general handyman can fix, as ina one person job or should I call out a window/glazing company?