Just depends. I oil mine maybe twice a year. That's with plenty of riding, sometimes I might do it more..but I really tear it apart and oil the crap out of it. I'll soap it with Murphy's Veg. Oil soap-love that stuff, before I oil and spot clean the sweat marks between thorough spring/fall cleaning/oiling. I just use plain neatsfoot oil, but I have a dark saddle and one I don't care if the light one gets dark.
I may not do it often enough or too much. LOL But that's how I do it and I oil REALLY WELL, both sides of my fenders, etc (western saddles) when I bother to do it. Keeps it nice and supple. But if you oil too often without cleaning, it promotes mold/mildew, depending on your climate. If you are in a humid area, you may not oil much, or in dry areas, need to more often.
I'll strip my Western saddle down once a year to get into anyplace that I can get to. That means up and under the skirt and jockey, taking the leathers and fenders down from their place, stirrups off, etc.. I'll use a paint brush and a spray bottle to get at the parts that are difficult to reach. I'll also take that time to check the screws and tighten up anything that seems loose.
In between, I use saddle soap to keep it from getting stiff from horse sweat (and mine too). I do the same but more often with my bridles and reins. Since I like spending time in the barn I probably do it more often then most people but I also ride every day. Some of my using tack is over 15 years old but is in perfect and supple condition.
If this is a brand new saddle, you want to remove the "protective coating' first with water and a rag... then oil the heck out of it... 3 or 4 times and be sure to get EVERYWHERE... Otherwise, wiping it off after each use, and oiling a few times a year is sufficient... I happen to LOVE to clean my saddle so I do it more often and it is as soft as butter.