Can I erect a barrier to keep water out of my garage?
Strangely enough, I have had to deal with this same problem a few times. Short of raising the garage or pouring a second higher floor, the solution is in the driveway.  We had to excavate apx 6 feet of asphalt and create a gradual dip draining away from the house and garage to exit water. Obviously, they screwed up big time when the driveway was installed. Installing drains in the garage won't work, especially in freezing, thawing etc. All you will get is an ice covered floor.  The only solution is to stop the water from getting in. That is going to mean reforming the driveway to self drain away, not into you garage. There is no quick cheap solution to your problem. Gravity rules!