I only clip wet now and never have any issues. My clippers stay COOLER vs when I do clip a dry face they heat up quickly. For me, the process is to double shampoo (I use dawn) one third of the body (neck and shoulder, belly, butt) with a jelly scrubber which gets super clean, quick sponge with apple cider vinegar water, then sponge with oil water (currently using shapleys light oil), sweat scrape off, walk to cross ties, light spray of the Pink Stuff, get to clipping!
This goes much faster for me than bathing, drying, then clipping + cooler blades + my blades stay sharper longer. I tend to use the ceramic blades so rust isn’t so much of an issue. I rarely get any lines and the horses are so soft and shiny after. It’s also good to do one body part at a time when it’s cooler and you don’t have a heated wash rack/ water.