I wipe it down with warm water first. Then warm water / and glycerin soap (saddle soap). Towel off the soap and a lot of dirt comes off. I can then either leave as is, or add Lexol. I will occasionally lightly dress with pure Neatsfoot oil, but NOT EVERY TIME and NOT ON THE LEATHERS. It is not good for leather to be oiled too much. Oiling the leathers will encourage them to stretch too much and over oiling will encourage rot.
Lastly, I top dress with glycerin soap, but very little water. Rub it on in circular motion, and buff to a shine. This layer acts as a barrier to dirt and helps to keep the tack from drying out. Leather is skin, and if you keep it in a hot , dry place, the moisture will evaporate out. Top dressing with glycering helps to prevent this. Do not overdo it on the reins as it will make them slippery.