Your pilots have real-time weather radar and reports and will make every practical attempt to safely arrive at your desired airport.
Your pilots will relay any information as they are made aware should the weather deteriorate below their operating minimums. They will alert you should you have to divert, much like airline flights, to a nearby airport that has suitable weather.
All flights are operated by FAA Part 135 Air Carriers or their foreign Civil Aviation Authority (CAA) equivalent which operate and exercise full operational control of all booked flights.