Minimum voltage/amperage required for peltier cooler?

I want to connect a couple of computer fans and a peltier cooler to some solar cells, but I want to keep the amount of electronics to a minimum (for the sake of KISS). Assuming the fans and peltier are rated to run at 12V, and I connect the solar cells to provide 12V at peak, will I be able to leave it connected all the time, i.e. when it's night time there is no electricity being provided, maybe in the late morning there is half the electricity, and in the afternoon sun full power?

I guess a simpler way to phrase my question is: Can these devices be run with much lower voltage or amperage than they are rated for?

Actually, Peltier coolers tend to have some problems when running on the initial voltage as after some time they reach the maximum temperature difference and begin to simply heat up...
That's assuming you don't fit decent heatsinks.
Simple answer: yes