I have never used oil on my horses hooves, nor does the owner of the stable where I keep my horse. Every single one (other than his two stallions) of his and boarded horses spend 24/7 outdoors, rain or shine, dust or mud. None of them (save the perhaps some of the borded ones) ever get oil or any other sort of hoof treatment other than regular farrier visits and emergency care.
Horses feet are desined to be self maintaining, so fussing and fauning really doesnt help unless you know your horse is prone to a problem and you are doing a preventitive measure (even then, topical treatments should be a backup for feed supliments which will have a far greater effect on the foof itself and overall health). The only thing a healthy hoof should need is a good trim when they grow out and regular cleaning.
in the wild this may be the case but the moment you fence in a horse you remove all its natural lifestyle - it can no longer get out of the muddy ground so the feet get saturated in water and too much water leads to very soft feet and soles and then the stronger possibility of foot problems, thrush, abscess, splits and chips. Think how much easier it is to trim your own toe nails if you have soaked your feet in the bath first. Soft horn damages more easily.
In summer grass dries up and there is limited exposure to sufficient water to keep hoofs pliable. Many farriers & trimmers rasp far to much of the periople from the wall of the feet - removing the protective covering. Oiling replaces this.
I've had horses of my own and worked with horses for over 40 years and all have been oiled daily. Racehorses and school ponies. Stabled horses twice daily and they had the toughest feet of all as they worked mainly on the roads during the week. At least an hours steady trotting on tar seal five days a week.
My horses are currently barefoot - they get oiled daily, two have excellent feet but the filly has real TB feet, weak and prone to abscess. Shortly the Clydesdale will be shod as in the new year she will be under saddle, she slips too much without shoes. Most Clydesdale have horrible shaped feet - but not mine, perfectly circular in front and slightly oval behind, text book frog and never been lame in her 8½years.
Re Mud fever etc - it is certainly not necessary to clip out or wash legs - it is this that tends to encourage the skin to weaken and be a breeding ground for mudfever.
Don't brush wet mud, allow legs to dry naturally and brush dried mud off in the morning. Work wise the horse is not going to stress if it's legs are muddy. If there are any symptoms of Mudfever and related infections wash the area with Nizoral shampoo, wash well beyond the affected area. Mudfever, Greasy heel, Rain scald/rot all start initially with a fungal infection of the skin. Treat this first and foremost and rarely will the infection get worse. Leave scabs alone - picking off makes them bleed and allows bacteria to get in. You buy the Nizoral from a pharmacy, dilute with hand hot water lather up well and then leave to dry. Washing with an old face cloth will dislodge any scabs that the Nizoral has broken down. Allow to dry without rinsing.
To prevent mudfever feed a supplement that contains copper and zinc - both required for strong healthy skin. To help reduce the possibility start applying liquid parafin (aka BAby Oil) to the hair weekly work well in. This will disperse water more easily.