V-brakes work great in the winter in my years of using them -- I've never wanted discs.

As long as the brake you replace your current v-brake with is also a v-brake (linear pull) your lever should still work just the same.

If you really think your old v-brake is shot, you might try pulling the little spring off of the brake arm on the side that isn't holding any tension and physically bending it outward to get more tension. I've done it on several old v-brakes and older road brakes with success.

HTH