If the wood is a species that will want to warp or crack a lot, you are better off keeping it on the log form for a time to lose the initial moisture while the movement is locked up, then sawing it will usually give more stable material. Taking off the bark can help in keeping out the bugs. If you only need smaller stock for something, movement isn't such a problem. The majority of woods that are known as suitable for woodworking, you can usually saw up quickly, but better to take movement into consideration, and have oversize thickness from the saw, and additional length for cracking. Air drying outside, but before beginning the project, bringing the wood inside will have it usually drop another percentage or two in moisture content. One or two points can make a big difference, stabilizing to the atmosphere. Not a bad idea to rough out your parts when you bring it inside, but even something that has been air drying for a number of years outside, can get some end checking, especially if a breeze through an open window or something, contacts it. Slow procedure is the best, bring it inside for a couple weeks, then rough the parts out and have them sit like that for a bit more time. Leave some extra length. Many times you can get away with making finish parts immediately after bringing inside, but it is a little risky, and if you aren't in a hurry, cut the wood some slack and let it do what it wants to do. It refuses to listen to commands is something I learned a long time ago.
Rounds are tough to dry. I think the best way is to completely cover them with a sealer to way slow down the drying process, and have them sitting inside with minimal air movement. Dry as slow as possible. Some day when you remember that you have them, you might find that they are then dry and haven't cracked. If that doesn't suit your needs, one slice from the outside down into the center, will often allow the movement without cracking (much). It's the way timber framers will sometimes use greener lumber, put a saw kerf into the wood that will absorb the expansion, then often fill the gap in later. If they are real nice rounds, I don't think the slice is so bad, if it's the only way you can get something without ugly cracks. I don't think I would fill in the gap on a round...maybe if it could come out looking ok.
Moisture in wood is a real nemesis, something only time to dry without question can remedy. Slow drying can allow success when the fibers have an easier time of it adjusting to the transition.