First of all, a huge
to you for stopping and staying at the scene to help everyone involved, including the person who ran a red light. I can tell you from dealing with these things every single day that it's rare that witnesses stop to be identified, and even more rare that they actually help...especially the person they know/thought was at fault.
It's easy to play armchair quarterback and second guess what someone does or say "I'd react in x or y way". Reality is that when confronted with a situation like that when you have a split second to react, you can't say for sure what your reaction may be. So while the driver who ran the red light is at fault, it's hard to second guess and say they made the wrong decision by trying to gun it and get through.
Driving on snow and controlling a car during a drift, yes, you steer into a skid/drift. However, all modern cars have ABS, and most of them have some form of stability control. With these cars, the best thing you can do in snow/ice if faced with an emergency stop or turn is stomp the brake pedal and steer. Let the cars' computers control the brakes and stop you from spinning...it'll do a 100x better job than you can. That's counterintuitive to what anyone over the age of 30 was brought up to do...we were always taught differently. But technology has changed, a lot. If you have a newer car with these things in them, stomp and steer.