I haven't had a whole replacement, but I did have knee surgery a couple of summers ago (in my mid 30's) - repairing a torn meniscus that caused my knee to lock up when I bent it. I visited Disney just before the surgery and again about three months, and had no real problems, other than some achy days from too much walking. I was wearing a knee brace before, and still occasionally do now, and one thing that helped was requesting one of the "accessible" rooms, so that it had a walk-in shower rather than the tub/shower combo that you have to bend your knee to climb into. Overall, I think I had an easier time of it at Disney post-surgery than pre-surgery.
A whole replacement is a bit more complicated, I'm told, but you're still up and moving around really fast. My FIL had a hip replaced a month ago and they had him up and walking (with a walker) the next day...and he's in his 70's. Now, he's moving WAY better than he did pre-replacement, although they still won't let him bend the hip to 90% or more. Theoretically, someone younger should recover at least as quickly...