If your husband does not have collision coverage, then he does not have coverage for an at-fault accident. Typically single vehicle accidents (including swerving to avoid a deer) is considered at fault.
Since the other driver is at fault in the accident, you will want to file a claim with his insurance company. They would be the ones that will pay for your damages. Here is more information on what to expect when you file a claim.
If your son hit a deer and that is what caused him to go into the ditch then the accident is likely to be considered a comprehensive claim rather than a collision. Comprehensive claims generally don't impact rates as severely, if at all, the way a collision claim would if he had hit another driver.
Animals cause all sorts of damage to vehicles, and not always because someone hits them with their car. Luckily, insurance companies don't discriminate over you hitting an animal or an animal hitting your car.