Do you think the mama bird could actually have time to escape once the snake sticks his head in there? How about mounting the house on a greased pole or hang it from some kind of rig that a snake can't climb down?
I don't think that squirrel-proof is possible using ordinary materials. Some time back I made eight or ten really nice (if I do say so myself) bird houses in octagon and hexagon shapes. I even gave them copper roofs -- built to last. Yeah, last until the gray squirrels discovered that they could chew right through that good cedar wood and enlarge the bird-sized holes to suit themselves. The last of them succumbed (the bird houses, not the squirrels) after about three years. The first time I looked into one of those enlarged holes and saw those beady black eyes staring back at me...
.>>>.. -- built to last. Yeah, last until the gray squirrels discovered that they could chew right through that good cedar wood and enlarge the bird-sized holes to suit themselves.
One hole enlargement prevention is to cut a square of metal with a hole the size of the hole in the birdhouse. Fasten that to the front of the birdhouse. Could be copper or painted steel. Squirrels and other birds that enlarge holes will be discouraged.
Around here, raccoons are another problem for bluebird houses. They can reach inside the hole and grab eggs and little birds for a snack. I sometimes make a 5" cylinder of 1/2" hardware cloth and make 1" four cuts on one end to bend outwards to make tabs that I fasten to the front of the birdhouse with screws. These cylinders are the same size or a bit larger than the required hole size. The birds don't seem to mind. The raccoons can't get their arms in enough to bend down to reach the baby birds. This may stop squirrels tool
Don't know what would work for snakes. A disk on the bottom of the birdhouse and on top the pole with a bed of sharp steel spikes pointed downwards?