In the winter I want to turn on my faucets a trickle to prevent pipes from
freezing. However, faucets are not designed to meter small amounts of water
flow, so it is tricky to let out small amounts of water from both hot and
cold sides. It's even trickier for single handle faucets -- they are not
balanced with small amount of water flow, so centering the handle does not
let out equal amounts of hot/cold water. And the hardest is to make everyone
do this after using the faucets.

Are there special faucets to help ease this task? Ideally this special
faucet would be separate from the regular faucet, have adjustable flow rate
independent from the on/off valve, and can be installed under the sink and
drain into the P trap without a dripping sound.

I did not find such device on the web, perhaps because I don't know what it
is called.