Uh what. I hope you don't mean the ACL itself will heal up cause it won't, torn ligaments will never heal although your knee will settle down usually. It depends on the knee but yes some people can go without surgery but your knee will never be the same again.
Tore my meniscus and ACL at the same time and I was in a straight leg brace for 6 weeks after surgery. I have relatively loose ligaments so i couldn't do much without an ACL but if you have tighter ligaments you can do pretty well. I knew a kid that didn't know he tore his ACL for 3 weeks after and he was still using his tramp, skiing and running around.
But skiing on a torn ACL isn't the greatest idea. Get it fixed and start rehabbing and you won't regret it.