Mine squirmed and wiggled at first , but now they know I
am going to wash their face so they may as well sit still. They still squirm a little but not much.
I don't make much of a fuss about it , I just take them say, "Let's wash your face." and then do it. Once they learned I was going to do it , they stopped all ( well most of) the drama.
I use puppy wipes for their face after they eat and a nice warm wet ( but not soaking ) washcloth for the eyes. Just take it slow with the eyes. She actually likes when I wash her eyes. She likes the warm cloth I think.
Also I sometimes wash her eyes while we sit in front of the fire when she is sleepy...she doesn't seem to care at all then.