I'm a big hiker too.
I do a lot of hiking and climbing in winter. In May this year, as a conclusion to my winter hiking, I did a 42-mile challenge hike along a rocky, hilly segment of the AT. Finished the 42 miles in 12.5 hours. (This is a bi-annual event organized by my mountain club.) I had trained for that like mad all winter and early spring, and after that big event, I got onto the road bike and within 5 weeks I was able to leverage that fitness into a 300-mile 18.5 mph ride.
So what I'm saying is - the two activities are excellent cross-training for each other. If I can't ride during winter because of snow and ice on the roads, I'll be on the hiking trails - often doing hill-repeats on some tough climbs in my area.