Cows currently? Interesting... or were you flashing back to childhood. Re: mouse trap. I had a hole in the exterior wood shingles that I could not find and they were getting in in the winter. I constructed a trap like you mention, that is impossible for them to resist, and nearly impossible to fail unless the fastening comes loose.
I did this because I didn't want poisons in the house as my kids were toddler age, and also not a snap trap to splash their blood and germs around. I wanted them in a bucket so I would release them far away along field where there are no houses. There was a humane aspect to it at the time. In fact one time I put a small cup of water for them to drink with benevolent intent. I went out and found two in there when I got home and put them in the garage to take them away the next day. They knocked over the water and froze to death so I gave up on the humane route. After I got the entry to the house fixed, I put rodent stations on the outside of the house and shed building. No problem since.
The trap was as follows: A tall plastic kitchen garbage can with smooth sides. I think they can jump about 18 inches so you need 20+ for a foolproof trap. The lever to make them fall in the bucket is a paper towel tube, the standard 12 inch size, or wrapping paper tube cut down to 18 or so will also work. Smear peanut butter at the end of the tube on the "can" side to eject them into the can. To make a lever I used a pencil, masking tape, and bread ties. Tape the pencil at 1/3 the tubes length, perpendicular to the tube and X it around so the pencil does NOT turn **DO NOT go THRU the tube as it will block the mouse, tape to the top. Take the bread ties and make them into shape of a pipe clamp or letter Omega and tape the flat ends to the table. The bread ties should clamp the pencil but allow it to rotate freely. Now the with the long side of the tube over the bucket, and smearing peanut butter around the mouth of the tube on the exit side it's almost done. NOTE: The entrance must remain clean. Of course the peanut butter and 2/3 of the tube will drop down to the bucket due to weight. Counter weight the top of the entrance with washers or coins so that the tube doesn't tip until the mouse is almost at the end. Make sure the mouse had eazy access to the entrance. Make stairs out of boxes or such. With a barn, MH, you can probably make a contraption with PVC pipe, pipe clamps one size up, and a drum and you will catch em all in a few days.