Update:
When the winter rains came and greened up the grass in the nearby national forest, the deer problem all but went away. The deer ate my arugula, but who can begrudge Bambi a nice salad? At any rate, I notice that on the other side of the four foot fence the grass is eaten down to the ground. On the garden side of the fence it is about a foot high. So the fence or the sprayers have been making some difference.
I did learn that it's not good to let them freeze with water in them. It made a mess but maybe (I hope) didn't ruin both of them. So they are off until frosts have ceased for the season.