I traveled to Goa during Christmas break, and it was pretty smooth for me. I traveled by bike, and there was absolutely no checking anywhere. Any mode of transport is pretty much the same, if you travel by road. However, try to be away from the crowd and follow your personal safety measures, and you should be good. North Goa is usually crowded, in our case we had chosen Agonda, South Goa. Agonda was the least crowded place at that point in time, which is also the case usually too.