If you pee standing you lift the seat before you do so.
If you pee sitting you drop the seat before you do so.
Responsibility is shared equally, with the onus on the person performing the act at the time to do what's needed.
True since peeing is inherently gross...
Anyhow you're entitled to your own subjective opinions of what you find more or less gross but you'd have to present some kind of decent argument if you expect others to adopt a similar viewpoint. From my perspective what makes it gross is that some savages have a tendency to miss the bowl and not clean it up afterwards. Which is gross.
You should look before you sit anyway. God knows what the last user left behind. Especially if it's pubic moulting season.
Ah internet stuffs, I should have known. I have yet to see a toilet seat cover that makes a 100% seal so sure yes it would reduce the amount, much in the way wearing a helmet while holding a grenade going off will protect your head...
Also, using that theory you touching the toilet seat cover to put it down transfers it to your hands from the previous user and when you wash your hands you are releasing the bacteria people have placed there from their last usage back into the air from the tap water. You would also be releasing anything trapped in the air inside the bowl when you lift the seat to use it forcing that air to move in an upward direction due to the lid moving up and air displacement. Thus rushing it toward your receptive areas(mouth, nose, face in general). Seems like it could cause less direct contact with yourself if you use toilet, finish up, pants up belt on etc. then flush and go directly to wash hands. You would be out of the immediate area of new toilet flush spray and on your way out. Also would cause the particles which have been mystified and thrown up to have time to presumably settle on surfaces by the time the next person comes into use toilet.
So what is worse for you? Possibly some extra bacteria from your own body that more likely than not grown accustom to and will have less harmful effects on you. Or some strangers bubonic plague they have just left on the seat cover(disclosure I am not 100% sure if bubonic plague can be transmitted via absorption through hands or via air born particulates)
So ya, leave it how you finished with it.
I don't, because my bladder can cope just fine until morning. My wife, on the other hand, needs to go frequently. It's really not a big deal, but bear in mind that our bathroom has relatively large windows (with opaque glass) so there is always sufficient ambient light to avoid injuring oneself. Also bear in mind that if you're getting up in the middle of the night, you're likely quite groggy from sleep so a lifted toilet is something you might not notice.
There was a Questionable Content comic about this very thing a few years back (If you've never seen the comic, it's well worth taking a look).
PS: on the rare occasion that I might go in the dark, I would obviously sit down. Safer that way.