I am just the opposite of many of those who have posted in that I tend to play better when I ride. Not sure why that is, but some of my best rounds the last couple of years have been while riding.
That being said, I walk the majority of the rounds I play. I don't carry any more, I rely on my push cart, but I thoroughly enjoy walking. My home course is great for walking and I find it to be a great way to some much needed exercise in. Sometimes I even jog a bit between shots to get the heart rate up. I feel like the round feels more genuine when I walk, not to mention I can take some time to enjoy the nature around the course.
I do tend to ride at new courses, but I only play a handful of rounds at new courses each year.