Up in MI, we have a TON of car-deer accidents. Most of them come from deer running from the shoulders or the sides of the shoulders across traffic. In those cases, the whistles do nothing, we hit one deer that had the whistle my grandmother installed on her Tempo- jammed in it's nostril.
Some tips form the guides we drove with up in Manitoba- that really do work...
For deer in the middle of the road, you should be able to see them if you're paying attention- if you can, drive at them as you stop. If they move, they're going somewhere you're not. Deer don't know the 'you drive on the right' thing, and Murphy's Law states that whatever direction you go, they will go the same way.
Watch very carefully for turns and corners- you will see deer predominantly in two locations- on the road in turns, and in the ditches. Why? Salt. In the winter, we salt corners, and they tread up to the road to lick the salt. The shoulders hold salt from car-spray. During the summer, etc, they're in the ditches since that's where the most water is held, thus lush pants. Other than that- they run around without abandon like idiots.
It's not something that you can buy something to really avoid- we had those whistles before, and they didn't scare deer away. Even when I was running 31 trucks at a long-haul carrier in dispatch, we hit 2 deer. One truck had deer whistles, one didn't. If someone wants to stick them on the side of their fenders like mirrors and think they do something, cool. I just think they're a gimmick meant to illicit the exact response that you're displaying.
My thought- if they did indeed work, the insurance industry would offer to put them on vehicles, since a deer accident is handled as a comprehensive claim- they only get $50 back here in Michigan. I hit a semi truck rim in the road, bumped across the freeway by someone- same thing. Current repair bill is $2,200 of which they get $50 from me. If whistles worked, they'd pay you to put them on, as up here they spend a LOT of money on car-deer accident claims.