They are good at staying put. Was out last week on the ATV and parked right next to one. It didn't move until the dog came running up to see what I was doing.Better keep an eye out for fawns.
I try not to mow any more than necessary until August when the fawns are bigger and can follow 'momma' around. When newborn or for the first week to 10 days, they just lay hidden and won't move.
Easy to run one over. And that is one sick feeling....believe me.