last year for the first time when cleaning the snow up .It melted and ran under the gargage door and you could skate in there ,Was it because my rubber flap is gone .the snow was on each side of the door not in front of it .would anew flap stop the snow.
A new gasket on the bottom of the door won't really solve your problem. Sounds more like you have a grading issue that drains runoff in the driveway directly towards the garage. Until that is remedied, no gasket will keep the water out. What you're looking at is having the grade outside the garage door changed to slope 'away from' the garage, not towards it. Even if you can only change it for a few feet, and possibly install a drain at the lowest point to collect the water, that will help keep the garage dry. Any 'fix' you make should be designed with the heaviest rain you've seen in your area in mind.