Besides training, several people in each paddling party should carry a First Aid Kit of some sort. Hypothermia, at least the initial stages isn't all that uncommon on Spring, Fall, and Winter trips. Dress in layers and dress for full immersion, even if you never swim. When paddling with less experienced boaters, take a close look at their gear for suitability. Keep an eye out for them during the trip as well and be prepared to offer one of your outer layers if you can do so safely. Here is a decent article on Hypothermia. Drowning is another issue you may need to deal with. Don't take ANY chances. Even if the victim appears to recover 100%, insist they visit a hospital for a 24-hour evaluation period to avoid any chance of a Near Drowning death. Cuts and scrapes are pretty easy to deal with if you have a decent First Aid Kit, these typically are not life threatening. Dislocations are more difficult and definitely fall into the "Do No Harm" category. If you don't know how to properly reduce a dislocation - don't try! A better course of action is to immobilize and get them to a hospital ASAP. Broken bones need immobilization and proper evacuation. A good first aid course covers all of these common issues and a great deal more. Here is a comprehensive article on this subject: First Aid considerations - boating.