slight green tinge to water

remove top radiator hose or thermostat housing or both, start up car, feed freshwater garden hose into the inlet and watch the water come out of the thermostat housing / top hose while the engine is running. When it's clear, shut off car, top off and you're done. Draining and refilling will not flush it out. It's gotta cycle through and to make that happen the water pump should be turning (and thermostat open or removed) and to make that happen the engine has to be running.

Don't leave water in the radiator between races! The slow build up of rust could possibly pose a problem but  that's nothing compared to the fear of freezing.  If you should happen to leave it outside when it freezes you probably just bought yourself a new engine and maybe a radiator as well.
  Bring a Magic marker and masking/duck tape to the track with you..
  Write in big letters          NO WATER        and tape it over the tach untill you fill the radiator then tear it off.  Make it a habbit and you won't regret it..   (You'll also learn to carry water to the race track with you, a smart thing I promise you)..
  It's not so much now but at the end of the season and you come home worn out and maybe the car let you down again! So you shove it into the back yard and come spring you now have a reason not to go racing or a expense you hadn't planned on.. even if it never freezes the rust generated over the winter from water sitting in there will cause the car to run hust.. If it runs hot enough you can't simply flush the rust away completely!

Heater core?  Who still has one of those?  This past February at CMP I wish we still had ours (and the HVAC duct work) to make the defroster work.

FWIW, we added anti-freeze to our car last winter and then re-flushed the whole system again when racing season started up again this year.

We too have the heater.  The water valve is wired open and the fan has only high speed.  A simple toggle switch is all we have rather than the OE cables and levers.  If the windshield gets foggy on a rainy night, it will be worth the extra 5 lbs.  It also doubles as a second radiator if the car starts running hot.  Driver discomfort = cool engine.  Luckily, we haven't needed it for either purpose yet.

I store a V-8 Triumph in a place that sees -30C nighttime temps in winter....I just remove the lower rad hose and crank the engine for a few seconds

It might start at -30 but I've never tried...too much snow to shovel, gotta install a battery, winter gas, etc. What's it like driving a sports car in January?