The fastest way I've found to break in new skates (even customs!) is to find a public session at really warm indoor rink (in New England that used to be Skating Club of Boston,
, tie the laces fairly loosely and skate laps for the entire time. No jumps, no turns, no sins, just plain forward stroking. It might take two or three sessions to do it but after 4 to six hours, I was pretty good. The fastest I've ever broken in new skates was once when I did a Leukemia Skate-a-thon in May and knew that each lap was costing each of my sponsors $.10. Three and a half hours earned me over $400 and my skates were great.
But if I can't do that sort of thing, it takes a lot longer to get skates comfortable if I'm trying to do it on free skating ice and/or trying to work on skills beyond stroking at the same time. Sometimes it can be months before I can say that my skates feel "like mine." It depends on what I'm doing and how much I'm skating of course. I also think it takes longer to break in skates in the winter because my feet don't sweat as much as they do in warmer months so it takes longer for the leather to soften up and conform to my feet.
As for skating on outdoor ice, as it's been said, outdoor ice is generally rock-hard and a little gritty from the dust and dirt that blows around and freezes on the surface. Unless you hit it on a warm, sunny day, it's going to take more effort to "get into" the ice - and your edges are going to wear down faster, as if you were rubbing them with sandpaper. The bumps and ruts shake up your balance too so in general, you're not going to feel as secure as you would on indoor rink ice. It can still be fun to do, but it's not ideal for increasing the comfort level on your new skates.