I do it for the horses that are respectable in the trailer. Would not do it for one that doesn’t trailer well. Cover the saddle with a saddle cover, and if it is cold enough and the horse is not a trailer-sweater, cover with a fleece cooler. This keeps the saddle cover from coming off and adds an additional ‘protective layer’ to the tack.
If you have a martingale, either tape the ends with electric tape onto the chestpiece of the 'gale or tie it with twine, do not loop it through. Also make sure you secure the stirrups, either PC fashion or by one of the stirrup-clips.
I did it often in my stock with my PC horse – he was great to trailer.
Would not do it with my new gelding, who moves around quite a lot.