Hill climbing training for short distance races

The most important thing is to do whatever will build your sustainable power (watts) on the bike. This involves developing the fitness to put out high power over the length of your race, and developing the skill/judgment to do that on the type of course that you'll be riding -- many people find it harder to push high power on the flats than on climbs. Another important thing for flatter races is to learn how to translate your watts into as much speed as possible, i.e., riding hard in a good aero position. Two riders with the same power output and weight can perform quite differently if one can ride more aero than the other. Hills do not prepare you for that aspect of racing.

The best thing that you could do for your fitness for sprint-length races would be to include a healthy mix of longer and shorter interval workouts in your winter plan. Shorter intervals might include efforts of 2-5 minutes (total interval duration of 10-20 minutes), and longer intervals might include efforts of 10-30 minutes (total duration of 40-120 minutes). These are no picnic, but they will help you a lot, relative to just going out and riding. Biking is not like running where you'll likely come out ahead simply by running a lot. If your hills already give you intervals like this, then you're good. If not, then you might want to adjust. 

This is very true. I almost never ride up a hill of any sort in training, as I do just about all of my riding on the trainer (faster, simpler, more controlled, time flexible), and yet hills are my strength in races. Well, the uphill parts, that is.