The way most saddles are tanned these days, you don't need to use a huge amount of oil for general cleaning. If you have a newer saddle, you'll only need it to oil it a few times a year.
For breaking in a saddle, try this. Clean it really well, then let it sit for an hour. Most new saddles are coated in a protective wax that needs to be cleaned off before use. Once it is completely dry, put a light coat of oil on it. Don't use too much, or let it drip or run down the sides as this will stain the leather. Put the saddle in a black, airtight trash bag and place in a warm room ( make sure it is DRY heat, not humid heat or it will mold!). Don't place it in front of any direct heat sources, such as a heater either. Leave in the trashbag for 24-48 hours. The leather will absorb the oil and be unbelievably soft and supple. My parents used to own a tack shop, and we used to use this technique whenever we had an old, dry, cracked saddle on consignment. It would make them like new again!
I've spent most of my life riding horses. The rest I've just wasted.