During my 40s, 50s, and 60s I didn't notice much difference in my ability to run and my ability to recover from heavy runs. But, I began to notice differences in my 70s. Now, as an 80-year-old geezer I'm more sensitive to cold weather, and I need to wear more layers during the winter. When I was younger, I often ran in temperatures close to 0 (F). In fact, my PB for low temperature is -18 (F) and was made in Massachusetts when I was in my 40s. Now, I hesitate going out when temperatures are in the teens or below (notice that I said I "hesitate". I didn't say I don't go out). When I was younger, I didn't wear gloves until the temperature was below 15 (F), but now I wear gloves when the temperature goes below 40. I used to wear shorts until the temperature went below freezing, but, now, I switch to long pants when the temperature gets in the low 50s or high 40s (F).
Now that I'm older, my body doesn't handle stress as well as it used to, and I need more time to recover from a heavy run. The running literature recommends 48 hours between heavy runs. I'm finding out that 48 hours may not be enough time and that 72 hours would be better. I try to have two non-running days between my medium run and my long run, and I can tell that that extra day helps me prepare for the long run.
I'm running significantly slower than I did when I was younger, and I have to allow more time for my body to adjust to increases in distance or pace. I used to run 7 minute miles, and I now run about 20 minute miles, and I walk much of the distance. Also, I'm discovering that consistently getting enough sleep is more important now than it was in my younger years. Here is a great article on getting rest.
Even though I'm slower and do fewer miles each week, I still have the enjoyment from running that I had during my younger years, and I still look forward to my runs. Because of my experience in running, I have more "wisdom" about my running, and I'm more content to use time as part of my training. I have no (well, almost no) desire to push, push, push to quickly reach faster and longer runs. I'm content to slowly increase my distance and my speed.
I'm sure that we all will react differently to our running as we grow older. If we listen to our bodies, this aging shouldn't be a serious problem. Our bodies will tell us when we need to reduce the stress and get more rest. I think the biggest challenge will be the mental part of running. Instead of pushing, pushing, pushing to faster and longer runs, we will have to overcome those urges and listen to and obey our bodies. Constantly running at the upper limits of ones ability leads to injury, and for older runners the threshold for injury is thinner and is more easily penetrated.
The bottom-line to all of this is that as we grow older, our abilities and capacities to be active decrease. If we thus decrease the intensity of our activities, we can enjoy being active during our old age. In fact, we can enjoy our old age even more since we don't have many of the stresses of life that we had when we were younger. We need to learn how our bodies react to old age and to pain. In my case, I've lived an almost pain-free life, and I've come to recognize that pain is a danger signal to me. Your body is different than mine, and you may have pains that are "normal" and are pains that can be ignored. Be careful, though, in ignoring pain. I do believe that pain is a signal from your body that something has changed in your life-style and your body can't handle the stress it is receiving.
I'm finding out that growing old is a great time of life, not just in running but in all aspects of life. I've always enjoyed being Allen Leigh. Life is a grand adventure, and my older years are just new and exciting chapters in that adventure. My overall goal in running is to run a marathon at any pace at age 100 :) When my time to pass-on comes, I hope it is a stroke while I'm out running. I think that would be a great way to say good bye to this wonderful life and a great way to begin the next chapter of my grand adventure! Hmmm... maybe I'd better carry some ID with me [I now have RoadID on my shoes].
Jeff Galloway published a book called Running Until You're 100. I recommend it for details about running as you get older.