I get depressed for a different reason: by the time I get off the skis (now), everyone else here on the Island on the West Coast has been cycling all winter and is peaking for race season which starts in April. I get depressed because only now am I getting in more than an average of one or two rides per month and everyone's passing me! Last week, I think I finally got in three road rides and one MTB ride.
However, as I'm not a huge fan of spring skiing (I get bored on groomers and only dream of pow), at this time of year I really look forward to cycling.
As Volklgirl said, mountain biking can give you the same rush as skiing and the trails here can be extremely technical. If you're just starting out, joining a women's group could help ease you into it.
And as Altagirl pointed out, you can learn to excel at climbing (where races are won!) and love it.
Summertime trips can help alleviate the depression, too. My hubby and I have followed the Tour de France and the Giro d'Italia on our road bikes (combined with lots of wine), and taken countless mountain biking trips with friends.
Lastly, as has been pointed out, there's the southern hemisphere. I've been to Chile twice and Argentina once, and the summer cycling totally helped my shredding at altitude!
If we didn't have the break, maybe we wouldn't crave it as much...