Exterior trim is the framing that is on the outside of a house around windows and doors. When should you install it? Whenever you want, so long as there is not a rain storm expected.
Different types of houses, because of the materials they are built with, need different types of exterior trims. Different types of trips require different types of materials. Some exterior trims are going to require caulking, while others are simply going to require long nails so there can be penetration into the frame of the window or door, to secure the exterior trim.
You do not want to install exterior trim right before a rain storm. If you do, the caulking will not set, and there is a chance that whatever stain or paint you are using will run and not set. Additionally, some houses, because they are older or have varied surfaces, are going to require special treatment around the windows to prevent rain from getting between the window and the frame, and causing rot. Whatever type of exterior trim you are going to use, you must do it when it is sunny so you have a chance to solve all these problems before rain comes, which could damage the house if everything is not right.
Another time not to install exterior trim is right before getting new windows, new siding, a new roof, or doing any major construction on the house. The problem is that the exterior trim might get damaged in the process. Most contractors are very careful, but accidents do happen. The last thing you want is to install new exterior trims, only to have it ruined by other work.