What is wrong with Idling

[DWBOX2000]

I guess I have two questions. I went for a winter ride on Saturday before the snow came. Well it's here. I went to put my battery trickler (maintainer) and put on backwards. I was in a rush. Probably on for less than a minute. Now the trickler has a light that goes red when this happens, which it was red. So I unplugged and put back on again and the light is yellow which just means it is charging. Always does this when i don't put on for a few days. It eventually turns green. I guess my first question is what is the likely hood that i damaged anything electronic (Battery is new but not too worried if that needs to be replaced. How about the other stuff?

Now I turned the key just to see what lit (without turning over) and everything looks fine. I guess I won't know if I did any damage until I actually start. Now I can't (okay I wont) drive because there is a lot of snow outside. What is the problem with just starting and letting run until it reaches operating temperature?

Suggestions?
Thanks.