Oh mice can definitely live in the engine. It's my understanding that this is where they usually make their nest. We also live in the country, and this is just the reality we live with. When it gets cold outside, the mice are going to look for a warm place to live.
I agree that it's really gross. I found one in my drink one day and threw it out the window. Another time I was driving and saw a mouse on top of the windshield wipers. I screamed and really wanted to swerve or something to make it get off of my van!
My husband is the one who gets ride of the mice around here, so I'm not actually sure what to do. Just remember that it is totally normal, and he's more scared of you than you are of him.
ETA - Just read Julie W's response. Yes, moth balls! My husband put moth balls in the vents. He did that a couple of months ago, so I rarely even notice the smell anymore. I think it's working!