Riding a bicycle is not only a good way to get exercise, it is also a good way to get close to nature. You can bike on narrow trails that you couldn't go on in a car and might be too tiresome to walk. But if you are going to get close to nature while biking, you can't ride it like your in a race. You have to slow down and look around, enjoy the scenery, the sounds the smells. Listen to the birds singing. Watch the bees and butterflies collect nectar. Occasionally, get off the bike and take a break. Breath in fresh air. Feel the energy flowing around the trees, rocks, everything. Share your energy with the trees and animals and ask them to share their energy with you (you don't have to say it out loud, just in your head).  A water bike or snow bike works as well.  
    What about motorized rides like an ATV, dirt bike, or snowmobile? I don't think they would work as well. First, your moving too fast to really take in your surroundings in an effective way; second, the noise from the motor is blocking and countering the sounds and vibrations of nature so, except when you are completely stopped, you won't get the same results. Plus you don't get much exercise that way.